Fft
dct¶
function dct
val dct :
?type_:[`Two | `Three | `Four | `One] ->
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Return the Discrete Cosine Transform of arbitrary type sequence x.
Parameters
-
x : array_like The input array.
-
type : {1, 2, 3, 4}, optional Type of the DCT (see Notes). Default type is 2.
-
n : int, optional Length of the transform. If
n < x.shape[axis]
,x
is truncated. Ifn > x.shape[axis]
,x
is zero-padded. The default results inn = x.shape[axis]
. -
axis : int, optional Axis along which the dct is computed; the default is over the last axis (i.e.,
axis=-1
). -
norm : {None, 'ortho'}, optional Normalization mode (see Notes). Default is None.
-
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details.
Returns
- y : ndarray of real The transformed input array.
See Also
- idct : Inverse DCT
Notes
For a single dimension array x
, dct(x, norm='ortho')
is equal to
MATLAB dct(x)
.
For norm=None
, there is no scaling on dct
and the idct
is scaled by
1/N
where N
is the 'logical' size of the DCT. For norm='ortho'
both directions are scaled by the same factor 1/sqrt(N)
.
There are, theoretically, 8 types of the DCT, only the first 4 types are implemented in SciPy.'The' DCT generally refers to DCT type 2, and 'the' Inverse DCT generally refers to DCT type 3.
Type I
There are several definitions of the DCT-I; we use the following
(for norm=None
)
If norm='ortho'
, x[0]
and x[N-1]
are multiplied by a scaling
factor of :math:\sqrt{2}
, and y[k]
is multiplied by a scaling factor
f
.. note:: The DCT-I is only supported for input size > 1.
Type II
There are several definitions of the DCT-II; we use the following
(for norm=None
)
If norm='ortho'
, y[k]
is multiplied by a scaling factor f
which makes the corresponding matrix of coefficients orthonormal
(O @ O.T = np.eye(N)
).
Type III
There are several definitions, we use the following (for norm=None
)
or, for norm='ortho'
The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up
to a factor 2N
. The orthonormalized DCT-III is exactly the inverse of
the orthonormalized DCT-II.
Type IV
There are several definitions of the DCT-IV; we use the following
(for norm=None
)
If norm='ortho'
, y[k]
is multiplied by a scaling factor f
References
.. [1] 'A Fast Cosine Transform in One and Two Dimensions', by J.
Makhoul, IEEE Transactions on acoustics, speech and signal
processing
vol. 28(1), pp. 27-34,
:doi:10.1109/TASSP.1980.1163351
(1980).
.. [2] Wikipedia, 'Discrete cosine transform',
- https://en.wikipedia.org/wiki/Discrete_cosine_transform
Examples
The Type 1 DCT is equivalent to the FFT (though faster) for real, even-symmetrical inputs. The output is also real and even-symmetrical. Half of the FFT input is used to generate half of the FFT output:
>>> from scipy.fft import fft, dct
>>> fft(np.array([4., 3., 5., 10., 5., 3.])).real
array([ 30., -8., 6., -2., 6., -8.])
>>> dct(np.array([4., 3., 5., 10.]), 1)
array([ 30., -8., 6., -2.])
dctn¶
function dctn
val dctn :
?type_:[`Two | `Three | `Four | `One] ->
?s:[`Array_like_of_ints of Py.Object.t | `I of int] ->
?axes:[`Array_like_of_ints of Py.Object.t | `I of int] ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Return multidimensional Discrete Cosine Transform along the specified axes.
Parameters
-
x : array_like The input array.
-
type : {1, 2, 3, 4}, optional Type of the DCT (see Notes). Default type is 2.
-
s : int or array_like of ints or None, optional The shape of the result. If both
s
andaxes
(see below) are None,s
isx.shape
; ifs
is None butaxes
is not None, thens
isscipy.take(x.shape, axes, axis=0)
. Ifs[i] > x.shape[i]
, the ith dimension is padded with zeros. Ifs[i] < x.shape[i]
, the ith dimension is truncated to lengths[i]
. If any element ofs
is -1, the size of the corresponding dimension ofx
is used. -
axes : int or array_like of ints or None, optional Axes over which the DCT is computed. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see Notes). Default is None.
-
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details.
Returns
- y : ndarray of real The transformed input array.
See Also
- idctn : Inverse multidimensional DCT
Notes
For full details of the DCT types and normalization modes, as well as
references, see dct
.
Examples
>>> from scipy.fft import dctn, idctn
>>> y = np.random.randn(16, 16)
>>> np.allclose(y, idctn(dctn(y)))
True
dst¶
function dst
val dst :
?type_:[`Two | `Three | `Four | `One] ->
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Return the Discrete Sine Transform of arbitrary type sequence x.
Parameters
-
x : array_like The input array.
-
type : {1, 2, 3, 4}, optional Type of the DST (see Notes). Default type is 2.
-
n : int, optional Length of the transform. If
n < x.shape[axis]
,x
is truncated. Ifn > x.shape[axis]
,x
is zero-padded. The default results inn = x.shape[axis]
. -
axis : int, optional Axis along which the dst is computed; the default is over the last axis (i.e.,
axis=-1
). -
norm : {None, 'ortho'}, optional Normalization mode (see Notes). Default is None.
-
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details.
Returns
- dst : ndarray of reals The transformed input array.
See Also
- idst : Inverse DST
Notes
For a single dimension array x
.
For norm=None
, there is no scaling on the dst
and the idst
is
scaled by 1/N
where N
is the 'logical' size of the DST. For
norm='ortho'
both directions are scaled by the same factor
1/sqrt(N)
.
There are, theoretically, 8 types of the DST for different combinations of even/odd boundary conditions and boundary off sets [1]_, only the first 4 types are implemented in SciPy.
Type I
There are several definitions of the DST-I; we use the following
for norm=None
. DST-I assumes the input is odd around n=-1
and n=N
.
Note that the DST-I is only supported for input size > 1.
The (unnormalized) DST-I is its own inverse, up to a factor 2(N+1)
.
The orthonormalized DST-I is exactly its own inverse.
Type II
There are several definitions of the DST-II; we use the following for
norm=None
. DST-II assumes the input is odd around n=-1/2
and
n=N-1/2
; the output is odd around :math:k=-1
and even around k=N-1
if norm='ortho'
, y[k]
is multiplied by a scaling factor f
Type III
There are several definitions of the DST-III, we use the following (for
norm=None
). DST-III assumes the input is odd around n=-1
and even
around n=N-1
The (unnormalized) DST-III is the inverse of the (unnormalized) DST-II, up
to a factor 2N
. The orthonormalized DST-III is exactly the inverse of the
orthonormalized DST-II.
Type IV
There are several definitions of the DST-IV, we use the following (for
norm=None
). DST-IV assumes the input is odd around n=-0.5
and even
around n=N-0.5
The (unnormalized) DST-IV is its own inverse, up to a factor 2N
. The
orthonormalized DST-IV is exactly its own inverse.
References
.. [1] Wikipedia, 'Discrete sine transform',
- https://en.wikipedia.org/wiki/Discrete_sine_transform
dstn¶
function dstn
val dstn :
?type_:[`Two | `Three | `Four | `One] ->
?s:[`Array_like_of_ints of Py.Object.t | `I of int] ->
?axes:[`Array_like_of_ints of Py.Object.t | `I of int] ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Return multidimensional Discrete Sine Transform along the specified axes.
Parameters
-
x : array_like The input array.
-
type : {1, 2, 3, 4}, optional Type of the DST (see Notes). Default type is 2.
-
s : int or array_like of ints or None, optional The shape of the result. If both
s
andaxes
(see below) are None,s
isx.shape
; ifs
is None butaxes
is not None, thens
isscipy.take(x.shape, axes, axis=0)
. Ifs[i] > x.shape[i]
, the ith dimension is padded with zeros. Ifs[i] < x.shape[i]
, the ith dimension is truncated to lengths[i]
. If any element ofshape
is -1, the size of the corresponding dimension ofx
is used. -
axes : int or array_like of ints or None, optional Axes over which the DST is computed. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see Notes). Default is None.
-
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details.
Returns
- y : ndarray of real The transformed input array.
See Also
- idstn : Inverse multidimensional DST
Notes
For full details of the DST types and normalization modes, as well as
references, see dst
.
Examples
>>> from scipy.fft import dstn, idstn
>>> y = np.random.randn(16, 16)
>>> np.allclose(y, idstn(dstn(y)))
True
fft¶
function fft
val fft :
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the 1-D discrete Fourier Transform.
This function computes the 1-D n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [1]_.
Parameters
-
x : array_like Input array, can be complex.
-
n : int, optional Length of the transformed axis of the output. If
n
is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. Ifn
is not given, the length of the input along the axis specified byaxis
is used. -
axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used.
-
norm : {None, 'ortho'}, optional Normalization mode. Default is None, meaning no normalization on the forward transforms and scaling by
1/n
on theifft
. Fornorm='ortho'
, both directions are scaled by1/sqrt(n)
. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. See the notes below for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. See below for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axis
indicated by
axis
, or the last one ifaxis
is not specified.
Raises
IndexError
if axes
is larger than the last axis of x
.
See Also
-
ifft : The inverse of
fft
. -
fft2 : The 2-D FFT.
-
fftn : The N-D FFT.
-
rfftn : The N-D FFT of real input.
-
fftfreq : Frequency bins for given FFT parameters.
-
next_fast_len : Size to pad input to for most efficient transforms
Notes
FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform
(DFT) can be calculated efficiently, by using symmetries in the calculated
terms. The symmetry is highest when n
is a power of 2, and the transform
is therefore most efficient for these sizes. For poorly factorizable sizes,
scipy.fft
uses Bluestein's algorithm [2]_ and so is never worse than
O(n
log n
). Further performance improvements may be seen by zero-padding
the input using next_fast_len
.
If x
is a 1d array, then the fft
is equivalent to ::
y[k] = np.sum(x * np.exp(-2j * np.pi * k * np.arange(n)/n))
The frequency term f=k/n
is found at y[k]
. At y[n/2]
we reach
the Nyquist frequency and wrap around to the negative-frequency terms. So,
for an 8-point transform, the frequencies of the result are
[0, 1, 2, 3, -4, -3, -2, -1]. To rearrange the fft output so that the
zero-frequency component is centered, like [-4, -3, -2, -1, 0, 1, 2, 3],
use fftshift
.
Transforms can be done in single, double, or extended precision (long double) floating point. Half precision inputs will be converted to single precision and non-floating-point inputs will be converted to double precision.
If the data type of x
is real, a 'real FFT' algorithm is automatically
used, which roughly halves the computation time. To increase efficiency
a little further, use rfft
, which does the same calculation, but only
outputs half of the symmetrical spectrum. If the data are both real and
symmetrical, the dct
can again double the efficiency, by generating
half of the spectrum from half of the signal.
When overwrite_x=True
is specified, the memory referenced by x
may
be used by the implementation in any way. This may include reusing the
memory for the result, but this is in no way guaranteed. You should not
rely on the contents of x
after the transform as this may change in
future without warning.
The workers
argument specifies the maximum number of parallel jobs to
split the FFT computation into. This will execute independent 1-D
FFTs within x
. So, x
must be at least 2-D and the
non-transformed axes must be large enough to split into chunks. If x
is
too small, fewer jobs may be used than requested.
References
.. [1] Cooley, James W., and John W. Tukey, 1965, 'An algorithm for the machine calculation of complex Fourier series,' Math. Comput.
- 19: 297-301. .. [2] Bluestein, L., 1970, 'A linear filtering approach to the computation of discrete Fourier transform'. IEEE Transactions on Audio and Electroacoustics. 18 (4): 451-455.
Examples
>>> import scipy.fft
>>> scipy.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8))
array([-2.33486982e-16+1.14423775e-17j, 8.00000000e+00-1.25557246e-15j,
2.33486982e-16+2.33486982e-16j, 0.00000000e+00+1.22464680e-16j,
-1.14423775e-17+2.33486982e-16j, 0.00000000e+00+5.20784380e-16j,
1.14423775e-17+1.14423775e-17j, 0.00000000e+00+1.22464680e-16j])
In this example, real input has an FFT which is Hermitian, i.e., symmetric in the real part and anti-symmetric in the imaginary part:
>>> from scipy.fft import fft, fftfreq, fftshift
>>> import matplotlib.pyplot as plt
>>> t = np.arange(256)
>>> sp = fftshift(fft(np.sin(t)))
>>> freq = fftshift(fftfreq(t.shape[-1]))
>>> plt.plot(freq, sp.real, freq, sp.imag)
[<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>]
>>> plt.show()
fft2¶
function fft2
val fft2 :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the 2-D discrete Fourier Transform
This function computes the N-D discrete Fourier Transform over any axes in an M-D array by means of the Fast Fourier Transform (FFT). By default, the transform is computed over the last two axes of the input array, i.e., a 2-dimensional FFT.
Parameters
-
x : array_like Input array, can be complex
-
s : sequence of ints, optional Shape (length of each transformed axis) of the output (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). This corresponds ton
forfft(x, n)
. Along each axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. ifs
is not given, the shape of the input along the axes specified byaxes
is used. -
axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last two axes are used.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by
axes
, or the last two axes ifaxes
is not given.
Raises
ValueError
If s
and axes
have different length, or axes
not given and
len(s) != 2
.
IndexError
If an element of axes
is larger than than the number of axes of x
.
See Also
-
ifft2 : The inverse 2-D FFT.
-
fft : The 1-D FFT.
-
fftn : The N-D FFT.
-
fftshift : Shifts zero-frequency terms to the center of the array. For 2-D input, swaps first and third quadrants, and second and fourth quadrants.
Notes
fft2
is just fftn
with a different default for axes
.
The output, analogously to fft
, contains the term for zero frequency in
the low-order corner of the transformed axes, the positive frequency terms
in the first half of these axes, the term for the Nyquist frequency in the
middle of the axes and the negative frequency terms in the second half of
the axes, in order of decreasingly negative frequency.
See fftn
for details and a plotting example, and fft
for
definitions and conventions used.
Examples
>>> import scipy.fft
>>> x = np.mgrid[:5, :5][0]
>>> scipy.fft.fft2(x)
array([[ 50. +0.j , 0. +0.j , 0. +0.j , # may vary
0. +0.j , 0. +0.j ],
[-12.5+17.20477401j, 0. +0.j , 0. +0.j ,
0. +0.j , 0. +0.j ],
[-12.5 +4.0614962j , 0. +0.j , 0. +0.j ,
0. +0.j , 0. +0.j ],
[-12.5 -4.0614962j , 0. +0.j , 0. +0.j ,
0. +0.j , 0. +0.j ],
[-12.5-17.20477401j, 0. +0.j , 0. +0.j ,
0. +0.j , 0. +0.j ]])
fftfreq¶
function fftfreq
val fftfreq :
?d:[`F of float | `I of int | `Bool of bool | `S of string] ->
n:int ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Return the Discrete Fourier Transform sample frequencies.
The returned float array f
contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given a window length n
and a sample spacing d
::
f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (dn) if n is even f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (dn) if n is odd
Parameters
-
n : int Window length.
-
d : scalar, optional Sample spacing (inverse of the sampling rate). Defaults to 1.
Returns
- f : ndarray
Array of length
n
containing the sample frequencies.
Examples
>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
>>> fourier = np.fft.fft(signal)
>>> n = signal.size
>>> timestep = 0.1
>>> freq = np.fft.fftfreq(n, d=timestep)
>>> freq
array([ 0. , 1.25, 2.5 , ..., -3.75, -2.5 , -1.25])
fftn¶
function fftn
val fftn :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the N-D discrete Fourier Transform.
This function computes the N-D discrete Fourier Transform over any number of axes in an M-D array by means of the Fast Fourier Transform (FFT).
Parameters
-
x : array_like Input array, can be complex.
-
s : sequence of ints, optional Shape (length of each transformed axis) of the output (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). This corresponds ton
forfft(x, n)
. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. ifs
is not given, the shape of the input along the axes specified byaxes
is used. -
axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by
axes
, or by a combination ofs
andx
, as explained in the parameters section above.
Raises
ValueError
If s
and axes
have different length.
IndexError
If an element of axes
is larger than than the number of axes of x
.
See Also
-
ifftn : The inverse of
fftn
, the inverse N-D FFT. -
fft : The 1-D FFT, with definitions and conventions used.
-
rfftn : The N-D FFT of real input.
-
fft2 : The 2-D FFT.
-
fftshift : Shifts zero-frequency terms to centre of array.
Notes
The output, analogously to fft
, contains the term for zero frequency in
the low-order corner of all axes, the positive frequency terms in the
first half of all axes, the term for the Nyquist frequency in the middle
of all axes and the negative frequency terms in the second half of all
axes, in order of decreasingly negative frequency.
Examples
>>> import scipy.fft
>>> x = np.mgrid[:3, :3, :3][0]
>>> scipy.fft.fftn(x, axes=(1, 2))
array([[[ 0.+0.j, 0.+0.j, 0.+0.j], # may vary
[ 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]],
[[ 9.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]],
[[18.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]]])
>>> scipy.fft.fftn(x, (2, 2), axes=(0, 1))
array([[[ 2.+0.j, 2.+0.j, 2.+0.j], # may vary
[ 0.+0.j, 0.+0.j, 0.+0.j]],
[[-2.+0.j, -2.+0.j, -2.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]]])
>>> import matplotlib.pyplot as plt
>>> [X, Y] = np.meshgrid(2 * np.pi * np.arange(200) / 12,
... 2 * np.pi * np.arange(200) / 34)
>>> S = np.sin(X) + np.cos(Y) + np.random.uniform(0, 1, X.shape)
>>> FS = scipy.fft.fftn(S)
>>> plt.imshow(np.log(np.abs(scipy.fft.fftshift(FS))**2))
<matplotlib.image.AxesImage object at 0x...>
>>> plt.show()
fftshift¶
function fftshift
val fftshift :
?axes:[`Shape_tuple of Py.Object.t | `I of int] ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Shift the zero-frequency component to the center of the spectrum.
This function swaps half-spaces for all axes listed (defaults to all).
Note that y[0]
is the Nyquist component only if len(x)
is even.
Parameters
-
x : array_like Input array.
-
axes : int or shape tuple, optional Axes over which to shift. Default is None, which shifts all axes.
Returns
- y : ndarray The shifted array.
See Also
- ifftshift : The inverse of
fftshift
.
Examples
>>> freqs = np.fft.fftfreq(10, 0.1)
>>> freqs
array([ 0., 1., 2., ..., -3., -2., -1.])
>>> np.fft.fftshift(freqs)
array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.])
Shift the zero-frequency component only along the second axis:
>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
>>> freqs
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
>>> np.fft.fftshift(freqs, axes=(1,))
array([[ 2., 0., 1.],
[-4., 3., 4.],
[-1., -3., -2.]])
get_workers¶
function get_workers
val get_workers :
unit ->
Py.Object.t
Returns the default number of workers within the current context
Examples
>>> from scipy import fft
>>> fft.get_workers()
1
>>> with fft.set_workers(4):
... fft.get_workers()
4
hfft¶
function hfft
val hfft :
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.
Parameters
-
x : array_like The input array.
-
n : int, optional Length of the transformed axis of the output. For
n
output points,n//2 + 1
input points are necessary. If the input is longer than this, it is cropped. If it is shorter than this, it is padded with zeros. Ifn
is not given, it is taken to be2*(m-1)
, wherem
is the length of the input along the axis specified byaxis
. -
axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. Seefft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : ndarray
The truncated or zero-padded input, transformed along the axis
indicated by
axis
, or the last one ifaxis
is not specified. The length of the transformed axis isn
, or, ifn
is not given,2*m - 2
, wherem
is the length of the transformed axis of the input. To get an odd number of output points,n
must be specified, for instance, as2*m - 1
in the typical case,
Raises
IndexError
If axis
is larger than the last axis of a
.
See also
-
rfft : Compute the 1-D FFT for real input.
-
ihfft : The inverse of
hfft
. -
hfftn : Compute the N-D FFT of a Hermitian signal.
Notes
hfft
/ihfft
are a pair analogous to rfft
/irfft
, but for the
opposite case: here the signal has Hermitian symmetry in the time
domain and is real in the frequency domain. So, here, it's hfft
, for
which you must supply the length of the result if it is to be odd.
* even: ihfft(hfft(a, 2*len(a) - 2) == a
, within roundoff error,
* odd: ihfft(hfft(a, 2*len(a) - 1) == a
, within roundoff error.
Examples
>>> from scipy.fft import fft, hfft
>>> a = 2 * np.pi * np.arange(10) / 10
>>> signal = np.cos(a) + 3j * np.sin(3 * a)
>>> fft(signal).round(10)
array([ -0.+0.j, 5.+0.j, -0.+0.j, 15.-0.j, 0.+0.j, 0.+0.j,
-0.+0.j, -15.-0.j, 0.+0.j, 5.+0.j])
>>> hfft(signal[:6]).round(10) # Input first half of signal
array([ 0., 5., 0., 15., -0., 0., 0., -15., -0., 5.])
>>> hfft(signal, 10) # Input entire signal and truncate
array([ 0., 5., 0., 15., -0., 0., 0., -15., -0., 5.])
hfft2¶
function hfft2
val hfft2 :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Compute the 2-D FFT of a Hermitian complex array.
Parameters
-
x : array Input array, taken to be Hermitian complex.
-
s : sequence of ints, optional Shape of the real output.
-
axes : sequence of ints, optional Axes over which to compute the FFT.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. Seefft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : ndarray The real result of the 2-D Hermitian complex real FFT.
See Also
- hfftn : Compute the N-D discrete Fourier Transform for Hermitian complex input.
Notes
This is really just hfftn
with different default behavior.
For more details see hfftn
.
hfftn¶
function hfftn
val hfftn :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Compute the N-D FFT of Hermitian symmetric complex input, i.e., a signal with a real spectrum.
This function computes the N-D discrete Fourier Transform for a
Hermitian symmetric complex input over any number of axes in an
M-D array by means of the Fast Fourier Transform (FFT). In other
words, ihfftn(hfftn(x, s)) == x
to within numerical accuracy. (s
here is x.shape
with s[-1] = x.shape[-1] * 2 - 1
, this is necessary
for the same reason x.shape
would be necessary for irfft
.)
Parameters
-
x : array_like Input array.
-
s : sequence of ints, optional Shape (length of each transformed axis) of the output (
s[0]
refers to axis 0,s[1]
to axis 1, etc.).s
is also the number of input points used along this axis, except for the last axis, wheres[-1]//2+1
points of the input are used. Along any axis, if the shape indicated bys
is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. Ifs
is not given, the shape of the input along the axes specified by axes is used. Except for the last axis which is taken to be2*(m-1)
wherem
is the length of the input along that axis. -
axes : sequence of ints, optional Axes over which to compute the inverse FFT. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : ndarray
The truncated or zero-padded input, transformed along the axes
indicated by
axes
, or by a combination ofs
orx
, as explained in the parameters section above. The length of each transformed axis is as given by the corresponding element ofs
, or the length of the input in every axis except for the last one ifs
is not given. In the final transformed axis the length of the output whens
is not given is2*(m-1)
wherem
is the length of the final transformed axis of the input. To get an odd number of output points in the final axis,s
must be specified.
Raises
ValueError
If s
and axes
have different length.
IndexError
If an element of axes
is larger than than the number of axes of x
.
See Also
-
ihfftn : The inverse N-D FFT with real spectrum. Inverse of
hfftn
. -
fft : The 1-D FFT, with definitions and conventions used.
-
rfft : Forward FFT of real input.
Notes
For a 1-D signal x
to have a real spectrum, it must satisfy
the Hermitian property::
x[i] == np.conj(x[-i]) for all i
This generalizes into higher dimensions by reflecting over each axis in
-
turn::
x[i, j, k, ...] == np.conj(x[-i, -j, -k, ...]) for all i, j, k, ...
This should not be confused with a Hermitian matrix, for which the transpose is its own conjugate::
x[i, j] == np.conj(x[j, i]) for all i, j
The default value of s
assumes an even output length in the final
transformation axis. When performing the final complex to real
transformation, the Hermitian symmetry requires that the last imaginary
component along that axis must be 0 and so it is ignored. To avoid losing
information, the correct length of the real input must be given.
Examples
>>> import scipy.fft
>>> x = np.ones((3, 2, 2))
>>> scipy.fft.hfftn(x)
array([[[12., 0.],
[ 0., 0.]],
[[ 0., 0.],
[ 0., 0.]],
[[ 0., 0.],
[ 0., 0.]]])
idct¶
function idct
val idct :
?type_:[`Two | `Three | `Four | `One] ->
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Return the Inverse Discrete Cosine Transform of an arbitrary type sequence.
Parameters
-
x : array_like The input array.
-
type : {1, 2, 3, 4}, optional Type of the DCT (see Notes). Default type is 2.
-
n : int, optional Length of the transform. If
n < x.shape[axis]
,x
is truncated. Ifn > x.shape[axis]
,x
is zero-padded. The default results inn = x.shape[axis]
. -
axis : int, optional Axis along which the idct is computed; the default is over the last axis (i.e.,
axis=-1
). -
norm : {None, 'ortho'}, optional Normalization mode (see Notes). Default is None.
-
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details.
Returns
- idct : ndarray of real The transformed input array.
See Also
- dct : Forward DCT
Notes
For a single dimension array x
, idct(x, norm='ortho')
is equal to
MATLAB idct(x)
.
'The' IDCT is the IDCT-II, which is the same as the normalized DCT-III.
The IDCT is equivalent to a normal DCT except for the normalization and type. DCT type 1 and 4 are their own inverse and DCTs 2 and 3 are each other's inverses.
Examples
The Type 1 DCT is equivalent to the DFT for real, even-symmetrical inputs. The output is also real and even-symmetrical. Half of the IFFT input is used to generate half of the IFFT output:
>>> from scipy.fft import ifft, idct
>>> ifft(np.array([ 30., -8., 6., -2., 6., -8.])).real
array([ 4., 3., 5., 10., 5., 3.])
>>> idct(np.array([ 30., -8., 6., -2.]), 1)
array([ 4., 3., 5., 10.])
idctn¶
function idctn
val idctn :
?type_:[`Two | `Three | `Four | `One] ->
?s:[`Array_like_of_ints of Py.Object.t | `I of int] ->
?axes:[`Array_like_of_ints of Py.Object.t | `I of int] ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Return multidimensional Discrete Cosine Transform along the specified axes.
Parameters
-
x : array_like The input array.
-
type : {1, 2, 3, 4}, optional Type of the DCT (see Notes). Default type is 2.
-
s : int or array_like of ints or None, optional The shape of the result. If both
s
andaxes
(see below) are None,s
isx.shape
; ifs
is None butaxes
is not None, thens
isscipy.take(x.shape, axes, axis=0)
. Ifs[i] > x.shape[i]
, the ith dimension is padded with zeros. Ifs[i] < x.shape[i]
, the ith dimension is truncated to lengths[i]
. If any element ofs
is -1, the size of the corresponding dimension ofx
is used. -
axes : int or array_like of ints or None, optional Axes over which the IDCT is computed. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see Notes). Default is None.
-
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details.
Returns
- y : ndarray of real The transformed input array.
See Also
- dctn : multidimensional DCT
Notes
For full details of the IDCT types and normalization modes, as well as
references, see idct
.
Examples
>>> from scipy.fft import dctn, idctn
>>> y = np.random.randn(16, 16)
>>> np.allclose(y, idctn(dctn(y)))
True
idst¶
function idst
val idst :
?type_:[`Two | `Three | `Four | `One] ->
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Return the Inverse Discrete Sine Transform of an arbitrary type sequence.
Parameters
-
x : array_like The input array.
-
type : {1, 2, 3, 4}, optional Type of the DST (see Notes). Default type is 2.
-
n : int, optional Length of the transform. If
n < x.shape[axis]
,x
is truncated. Ifn > x.shape[axis]
,x
is zero-padded. The default results inn = x.shape[axis]
. -
axis : int, optional Axis along which the idst is computed; the default is over the last axis (i.e.,
axis=-1
). -
norm : {None, 'ortho'}, optional Normalization mode (see Notes). Default is None.
-
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details.
Returns
- idst : ndarray of real The transformed input array.
See Also
- dst : Forward DST
Notes
'The' IDST is the IDST-II, which is the same as the normalized DST-III.
The IDST is equivalent to a normal DST except for the normalization and type. DST type 1 and 4 are their own inverse and DSTs 2 and 3 are each other's inverses.
idstn¶
function idstn
val idstn :
?type_:[`Two | `Three | `Four | `One] ->
?s:[`Array_like_of_ints of Py.Object.t | `I of int] ->
?axes:[`Array_like_of_ints of Py.Object.t | `I of int] ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Return multidimensional Discrete Sine Transform along the specified axes.
Parameters
-
x : array_like The input array.
-
type : {1, 2, 3, 4}, optional Type of the DST (see Notes). Default type is 2.
-
s : int or array_like of ints or None, optional The shape of the result. If both
s
andaxes
(see below) are None,s
isx.shape
; ifs
is None butaxes
is not None, thens
isscipy.take(x.shape, axes, axis=0)
. Ifs[i] > x.shape[i]
, the ith dimension is padded with zeros. Ifs[i] < x.shape[i]
, the ith dimension is truncated to lengths[i]
. If any element ofs
is -1, the size of the corresponding dimension ofx
is used. -
axes : int or array_like of ints or None, optional Axes over which the IDST is computed. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see Notes). Default is None.
-
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details.
Returns
- y : ndarray of real The transformed input array.
See Also
- dstn : multidimensional DST
Notes
For full details of the IDST types and normalization modes, as well as
references, see idst
.
Examples
>>> from scipy.fft import dstn, idstn
>>> y = np.random.randn(16, 16)
>>> np.allclose(y, idstn(dstn(y)))
True
ifft¶
function ifft
val ifft :
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the 1-D inverse discrete Fourier Transform.
This function computes the inverse of the 1-D n-point
discrete Fourier transform computed by fft
. In other words,
ifft(fft(x)) == x
to within numerical accuracy.
The input should be ordered in the same way as is returned by fft
,
i.e.,
x[0]
should contain the zero frequency term,x[1:n//2]
should contain the positive-frequency terms,x[n//2 + 1:]
should contain the negative-frequency terms, in increasing order starting from the most negative frequency.
For an even number of input points, x[n//2]
represents the sum of
the values at the positive and negative Nyquist frequencies, as the two
are aliased together. See fft
for details.
Parameters
-
x : array_like Input array, can be complex.
-
n : int, optional Length of the transformed axis of the output. If
n
is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. Ifn
is not given, the length of the input along the axis specified byaxis
is used. See notes about padding issues. -
axis : int, optional Axis over which to compute the inverse DFT. If not given, the last axis is used.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axis
indicated by
axis
, or the last one ifaxis
is not specified.
Raises
IndexError
If axes
is larger than the last axis of x
.
See Also
-
fft : The 1-D (forward) FFT, of which
ifft
is the inverse. -
ifft2 : The 2-D inverse FFT.
-
ifftn : The N-D inverse FFT.
Notes
If the input parameter n
is larger than the size of the input, the input
is padded by appending zeros at the end. Even though this is the common
approach, it might lead to surprising results. If a different padding is
desired, it must be performed before calling ifft
.
If x
is a 1-D array, then the ifft
is equivalent to ::
y[k] = np.sum(x * np.exp(2j * np.pi * k * np.arange(n)/n)) / len(x)
As with fft
, ifft
has support for all floating point types and is
optimized for real input.
Examples
>>> import scipy.fft
>>> scipy.fft.ifft([0, 4, 0, 0])
array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) # may vary
Create and plot a band-limited signal with random phases:
>>> import matplotlib.pyplot as plt
>>> t = np.arange(400)
>>> n = np.zeros((400,), dtype=complex)
>>> n[40:60] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20,)))
>>> s = scipy.fft.ifft(n)
>>> plt.plot(t, s.real, 'b-', t, s.imag, 'r--')
[<matplotlib.lines.Line2D object at ...>, <matplotlib.lines.Line2D object at ...>]
>>> plt.legend(('real', 'imaginary'))
<matplotlib.legend.Legend object at ...>
>>> plt.show()
ifft2¶
function ifft2
val ifft2 :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the 2-D inverse discrete Fourier Transform.
This function computes the inverse of the 2-D discrete Fourier
Transform over any number of axes in an M-D array by means of
the Fast Fourier Transform (FFT). In other words, ifft2(fft2(x)) == x
to within numerical accuracy. By default, the inverse transform is
computed over the last two axes of the input array.
The input, analogously to ifft
, should be ordered in the same way as is
returned by fft2
, i.e., it should have the term for zero frequency
in the low-order corner of the two axes, the positive frequency terms in
the first half of these axes, the term for the Nyquist frequency in the
middle of the axes and the negative frequency terms in the second half of
both axes, in order of decreasingly negative frequency.
Parameters
-
x : array_like Input array, can be complex.
-
s : sequence of ints, optional Shape (length of each axis) of the output (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). This corresponds ton
forifft(x, n)
. Along each axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. ifs
is not given, the shape of the input along the axes specified byaxes
is used. See notes for issue onifft
zero padding. -
axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last two axes are used.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by
axes
, or the last two axes ifaxes
is not given.
Raises
ValueError
If s
and axes
have different length, or axes
not given and
len(s) != 2
.
IndexError
If an element of axes
is larger than than the number of axes of x
.
See Also
-
fft2 : The forward 2-D FFT, of which
ifft2
is the inverse. -
ifftn : The inverse of the N-D FFT.
-
fft : The 1-D FFT.
-
ifft : The 1-D inverse FFT.
Notes
ifft2
is just ifftn
with a different default for axes
.
See ifftn
for details and a plotting example, and fft
for
definition and conventions used.
Zero-padding, analogously with ifft
, is performed by appending zeros to
the input along the specified dimension. Although this is the common
approach, it might lead to surprising results. If another form of zero
padding is desired, it must be performed before ifft2
is called.
Examples
>>> import scipy.fft
>>> x = 4 * np.eye(4)
>>> scipy.fft.ifft2(x)
array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], # may vary
[0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],
[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],
[0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])
ifftn¶
function ifftn
val ifftn :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the N-D inverse discrete Fourier Transform.
This function computes the inverse of the N-D discrete
Fourier Transform over any number of axes in an M-D array by
means of the Fast Fourier Transform (FFT). In other words,
ifftn(fftn(x)) == x
to within numerical accuracy.
The input, analogously to ifft
, should be ordered in the same way as is
returned by fftn
, i.e., it should have the term for zero frequency
in all axes in the low-order corner, the positive frequency terms in the
first half of all axes, the term for the Nyquist frequency in the middle
of all axes and the negative frequency terms in the second half of all
axes, in order of decreasingly negative frequency.
Parameters
-
x : array_like Input array, can be complex.
-
s : sequence of ints, optional Shape (length of each transformed axis) of the output (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). This corresponds ton
forifft(x, n)
. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. ifs
is not given, the shape of the input along the axes specified byaxes
is used. See notes for issue onifft
zero padding. -
axes : sequence of ints, optional Axes over which to compute the IFFT. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by
axes
, or by a combination ofs
orx
, as explained in the parameters section above.
Raises
ValueError
If s
and axes
have different length.
IndexError
If an element of axes
is larger than than the number of axes of x
.
See Also
-
fftn : The forward N-D FFT, of which
ifftn
is the inverse. -
ifft : The 1-D inverse FFT.
-
ifft2 : The 2-D inverse FFT.
-
ifftshift : Undoes
fftshift
, shifts zero-frequency terms to beginning of array.
Notes
Zero-padding, analogously with ifft
, is performed by appending zeros to
the input along the specified dimension. Although this is the common
approach, it might lead to surprising results. If another form of zero
padding is desired, it must be performed before ifftn
is called.
Examples
>>> import scipy.fft
>>> x = np.eye(4)
>>> scipy.fft.ifftn(scipy.fft.fftn(x, axes=(0,)), axes=(1,))
array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], # may vary
[0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],
[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],
[0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])
Create and plot an image with band-limited frequency content:
>>> import matplotlib.pyplot as plt
>>> n = np.zeros((200,200), dtype=complex)
>>> n[60:80, 20:40] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20, 20)))
>>> im = scipy.fft.ifftn(n).real
>>> plt.imshow(im)
<matplotlib.image.AxesImage object at 0x...>
>>> plt.show()
ifftshift¶
function ifftshift
val ifftshift :
?axes:[`Shape_tuple of Py.Object.t | `I of int] ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
The inverse of fftshift
. Although identical for even-length x
, the
functions differ by one sample for odd-length x
.
Parameters
-
x : array_like Input array.
-
axes : int or shape tuple, optional Axes over which to calculate. Defaults to None, which shifts all axes.
Returns
- y : ndarray The shifted array.
See Also
- fftshift : Shift zero-frequency component to the center of the spectrum.
Examples
>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
>>> freqs
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
>>> np.fft.ifftshift(np.fft.fftshift(freqs))
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
ihfft¶
function ihfft
val ihfft :
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the inverse FFT of a signal that has Hermitian symmetry.
Parameters
-
x : array_like Input array.
-
n : int, optional Length of the inverse FFT, the number of points along transformation axis in the input to use. If
n
is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. Ifn
is not given, the length of the input along the axis specified byaxis
is used. -
axis : int, optional Axis over which to compute the inverse FFT. If not given, the last axis is used.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. Seefft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axis
indicated by
axis
, or the last one ifaxis
is not specified. The length of the transformed axis isn//2 + 1
.
See also
hfft, irfft
Notes
hfft
/ihfft
are a pair analogous to rfft
/irfft
, but for the
opposite case: here, the signal has Hermitian symmetry in the time
domain and is real in the frequency domain. So, here, it's hfft
, for
which you must supply the length of the result if it is to be odd:
* even: ihfft(hfft(a, 2*len(a) - 2) == a
, within roundoff error,
* odd: ihfft(hfft(a, 2*len(a) - 1) == a
, within roundoff error.
Examples
>>> from scipy.fft import ifft, ihfft
>>> spectrum = np.array([ 15, -4, 0, -1, 0, -4])
>>> ifft(spectrum)
array([1.+0.j, 2.+0.j, 3.+0.j, 4.+0.j, 3.+0.j, 2.+0.j]) # may vary
>>> ihfft(spectrum)
array([ 1.-0.j, 2.-0.j, 3.-0.j, 4.-0.j]) # may vary
ihfft2¶
function ihfft2
val ihfft2 :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Compute the 2-D inverse FFT of a real spectrum.
Parameters
-
x : array_like The input array
-
s : sequence of ints, optional Shape of the real input to the inverse FFT.
-
axes : sequence of ints, optional The axes over which to compute the inverse fft. Default is the last two axes.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : ndarray The result of the inverse real 2-D FFT.
See Also
- ihfftn : Compute the inverse of the N-D FFT of Hermitian input.
Notes
This is really ihfftn
with different defaults.
For more details see ihfftn
.
ihfftn¶
function ihfftn
val ihfftn :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the N-D inverse discrete Fourier Transform for a real spectrum.
This function computes the N-D inverse discrete Fourier Transform over any number of axes in an M-D real array by means of the Fast Fourier Transform (FFT). By default, all axes are transformed, with the real transform performed over the last axis, while the remaining transforms are complex.
Parameters
-
x : array_like Input array, taken to be real.
-
s : sequence of ints, optional Shape (length along each transformed axis) to use from the input. (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. ifs
is not given, the shape of the input along the axes specified byaxes
is used. -
axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by
axes
, or by a combination ofs
andx
, as explained in the parameters section above. The length of the last axis transformed will bes[-1]//2+1
, while the remaining transformed axes will have lengths according tos
, or unchanged from the input.
Raises
ValueError
If s
and axes
have different length.
IndexError
If an element of axes
is larger than than the number of axes of x
.
See Also
-
hfftn : The forward N-D FFT of Hermitian input.
-
hfft : The 1-D FFT of Hermitian input.
-
fft : The 1-D FFT, with definitions and conventions used.
-
fftn : The N-D FFT.
-
hfft2 : The 2-D FFT of Hermitian input.
Notes
The transform for real input is performed over the last transformation
axis, as by ihfft
, then the transform over the remaining axes is
performed as by ifftn
. The order of the output is the positive part of
the Hermitian output signal, in the same format as rfft
.
Examples
>>> import scipy.fft
>>> x = np.ones((2, 2, 2))
>>> scipy.fft.ihfftn(x)
array([[[1.+0.j, 0.+0.j], # may vary
[0.+0.j, 0.+0.j]],
[[0.+0.j, 0.+0.j],
[0.+0.j, 0.+0.j]]])
>>> scipy.fft.ihfftn(x, axes=(2, 0))
array([[[1.+0.j, 0.+0.j], # may vary
[1.+0.j, 0.+0.j]],
[[0.+0.j, 0.+0.j],
[0.+0.j, 0.+0.j]]])
irfft¶
function irfft
val irfft :
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Computes the inverse of rfft
.
This function computes the inverse of the 1-D n-point
discrete Fourier Transform of real input computed by rfft
.
In other words, irfft(rfft(x), len(x)) == x
to within numerical
accuracy. (See Notes below for why len(a)
is necessary here.)
The input is expected to be in the form returned by rfft
, i.e., the
real zero-frequency term followed by the complex positive frequency terms
in order of increasing frequency. Since the discrete Fourier Transform of
real input is Hermitian-symmetric, the negative frequency terms are taken
to be the complex conjugates of the corresponding positive frequency terms.
Parameters
-
x : array_like The input array.
-
n : int, optional Length of the transformed axis of the output. For
n
output points,n//2+1
input points are necessary. If the input is longer than this, it is cropped. If it is shorter than this, it is padded with zeros. Ifn
is not given, it is taken to be2*(m-1)
, wherem
is the length of the input along the axis specified byaxis
. -
axis : int, optional Axis over which to compute the inverse FFT. If not given, the last axis is used.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : ndarray
The truncated or zero-padded input, transformed along the axis
indicated by
axis
, or the last one ifaxis
is not specified. The length of the transformed axis isn
, or, ifn
is not given,2*(m-1)
wherem
is the length of the transformed axis of the input. To get an odd number of output points,n
must be specified.
Raises
IndexError
If axis
is larger than the last axis of x
.
See Also
-
rfft : The 1-D FFT of real input, of which
irfft
is inverse. -
fft : The 1-D FFT.
-
irfft2 : The inverse of the 2-D FFT of real input.
-
irfftn : The inverse of the N-D FFT of real input.
Notes
Returns the real valued n
-point inverse discrete Fourier transform
of x
, where x
contains the non-negative frequency terms of a
Hermitian-symmetric sequence. n
is the length of the result, not the
input.
If you specify an n
such that a
must be zero-padded or truncated, the
extra/removed values will be added/removed at high frequencies. One can
thus resample a series to m
points via Fourier interpolation by:
a_resamp = irfft(rfft(a), m)
.
The default value of n
assumes an even output length. By the Hermitian
symmetry, the last imaginary component must be 0 and so is ignored. To
avoid losing information, the correct length of the real input must be
given.
Examples
>>> import scipy.fft
>>> scipy.fft.ifft([1, -1j, -1, 1j])
array([0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]) # may vary
>>> scipy.fft.irfft([1, -1j, -1])
array([0., 1., 0., 0.])
Notice how the last term in the input to the ordinary ifft
is the
complex conjugate of the second term, and the output has zero imaginary
part everywhere. When calling irfft
, the negative frequencies are not
specified, and the output array is purely real.
irfft2¶
function irfft2
val irfft2 :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Computes the inverse of rfft2
Parameters
-
x : array_like The input array
-
s : sequence of ints, optional Shape of the real output to the inverse FFT.
-
axes : sequence of ints, optional The axes over which to compute the inverse fft. Default is the last two axes.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : ndarray The result of the inverse real 2-D FFT.
See Also
-
rfft2 : The 2-D FFT of real input.
-
irfft : The inverse of the 1-D FFT of real input.
-
irfftn : The inverse of the N-D FFT of real input.
Notes
This is really irfftn
with different defaults.
For more details see irfftn
.
irfftn¶
function irfftn
val irfftn :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Computes the inverse of rfftn
This function computes the inverse of the N-D discrete
Fourier Transform for real input over any number of axes in an
M-D array by means of the Fast Fourier Transform (FFT). In
other words, irfftn(rfftn(x), x.shape) == x
to within numerical
accuracy. (The a.shape
is necessary like len(a)
is for irfft
,
and for the same reason.)
The input should be ordered in the same way as is returned by rfftn
,
i.e., as for irfft
for the final transformation axis, and as for ifftn
along all the other axes.
Parameters
-
x : array_like Input array.
-
s : sequence of ints, optional Shape (length of each transformed axis) of the output (
s[0]
refers to axis 0,s[1]
to axis 1, etc.).s
is also the number of input points used along this axis, except for the last axis, wheres[-1]//2+1
points of the input are used. Along any axis, if the shape indicated bys
is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. Ifs
is not given, the shape of the input along the axes specified by axes is used. Except for the last axis which is taken to be2*(m-1)
, wherem
is the length of the input along that axis. -
axes : sequence of ints, optional Axes over which to compute the inverse FFT. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : ndarray
The truncated or zero-padded input, transformed along the axes
indicated by
axes
, or by a combination ofs
orx
, as explained in the parameters section above. The length of each transformed axis is as given by the corresponding element ofs
, or the length of the input in every axis except for the last one ifs
is not given. In the final transformed axis the length of the output whens
is not given is2*(m-1)
, wherem
is the length of the final transformed axis of the input. To get an odd number of output points in the final axis,s
must be specified.
Raises
ValueError
If s
and axes
have different length.
IndexError
If an element of axes
is larger than than the number of axes of x
.
See Also
-
rfftn : The forward N-D FFT of real input, of which
ifftn
is the inverse. -
fft : The 1-D FFT, with definitions and conventions used.
-
irfft : The inverse of the 1-D FFT of real input.
-
irfft2 : The inverse of the 2-D FFT of real input.
Notes
See fft
for definitions and conventions used.
See rfft
for definitions and conventions used for real input.
The default value of s
assumes an even output length in the final
transformation axis. When performing the final complex to real
transformation, the Hermitian symmetry requires that the last imaginary
component along that axis must be 0 and so it is ignored. To avoid losing
information, the correct length of the real input must be given.
Examples
>>> import scipy.fft
>>> x = np.zeros((3, 2, 2))
>>> x[0, 0, 0] = 3 * 2 * 2
>>> scipy.fft.irfftn(x)
array([[[1., 1.],
[1., 1.]],
[[1., 1.],
[1., 1.]],
[[1., 1.],
[1., 1.]]])
register_backend¶
function register_backend
val register_backend :
[`PyObject of Py.Object.t | `Scipy] ->
Py.Object.t
Register a backend for permanent use.
Registered backends have the lowest priority and will be tried after the global backend.
Parameters
- backend: {object, 'scipy'}
The backend to use.
Can either be a
str
containing the name of a known backend {'scipy'} or an object that implements the uarray protocol.
Raises
- ValueError: If the backend does not implement
numpy.scipy.fft
.
Examples
We can register a new fft backend:
>>> from scipy.fft import fft, register_backend, set_global_backend
>>> class NoopBackend: # Define an invalid Backend
... __ua_domain__ = 'numpy.scipy.fft'
... def __ua_function__(self, func, args, kwargs):
... return NotImplemented
>>> set_global_backend(NoopBackend()) # Set the invalid backend as global
>>> register_backend('scipy') # Register a new backend
>>> fft([1]) # The registered backend is called because the global backend returns `NotImplemented`
array([1.+0.j])
>>> set_global_backend('scipy') # Restore global backend to default
rfft¶
function rfft
val rfft :
?n:int ->
?axis:int ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:Py.Object.t ->
unit ->
Py.Object.t
Compute the 1-D discrete Fourier Transform for real input.
This function computes the 1-D n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).
Parameters
-
a : array_like Input array
-
n : int, optional Number of points along transformation axis in the input to use. If
n
is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. Ifn
is not given, the length of the input along the axis specified byaxis
is used. -
axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axis
indicated by
axis
, or the last one ifaxis
is not specified. Ifn
is even, the length of the transformed axis is(n/2)+1
. Ifn
is odd, the length is(n+1)/2
.
Raises
IndexError
If axis
is larger than the last axis of a
.
See Also
-
irfft : The inverse of
rfft
. -
fft : The 1-D FFT of general (complex) input.
-
fftn : The N-D FFT.
-
rfft2 : The 2-D FFT of real input.
-
rfftn : The N-D FFT of real input.
Notes
When the DFT is computed for purely real input, the output is
Hermitian-symmetric, i.e., the negative frequency terms are just the complex
conjugates of the corresponding positive-frequency terms, and the
negative-frequency terms are therefore redundant. This function does not
compute the negative frequency terms, and the length of the transformed
axis of the output is therefore n//2 + 1
.
When X = rfft(x)
and fs is the sampling frequency, X[0]
contains
the zero-frequency term 0*fs, which is real due to Hermitian symmetry.
If n
is even, A[-1]
contains the term representing both positive
and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely
real. If n
is odd, there is no term at fs/2; A[-1]
contains
the largest positive frequency (fs/2*(n-1)/n), and is complex in the
general case.
If the input a
contains an imaginary part, it is silently discarded.
Examples
>>> import scipy.fft
>>> scipy.fft.fft([0, 1, 0, 0])
array([ 1.+0.j, 0.-1.j, -1.+0.j, 0.+1.j]) # may vary
>>> scipy.fft.rfft([0, 1, 0, 0])
array([ 1.+0.j, 0.-1.j, -1.+0.j]) # may vary
Notice how the final element of the fft
output is the complex conjugate
of the second element, for real input. For rfft
, this symmetry is
exploited to compute only the non-negative frequency terms.
rfft2¶
function rfft2
val rfft2 :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Compute the 2-D FFT of a real array.
Parameters
-
x : array Input array, taken to be real.
-
s : sequence of ints, optional Shape of the FFT.
-
axes : sequence of ints, optional Axes over which to compute the FFT.
-
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : ndarray The result of the real 2-D FFT.
See Also
-
irfft2 : The inverse of the 2-D FFT of real input.
-
rfft : The 1-D FFT of real input.
-
rfftn : Compute the N-D discrete Fourier Transform for real input.
Notes
This is really just rfftn
with different default behavior.
For more details see rfftn
.
rfftfreq¶
function rfftfreq
val rfftfreq :
?d:[`F of float | `I of int | `Bool of bool | `S of string] ->
n:int ->
unit ->
[`ArrayLike|`Ndarray|`Object] Np.Obj.t
Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft).
The returned float array f
contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given a window length n
and a sample spacing d
::
f = [0, 1, ..., n/2-1, n/2] / (dn) if n is even f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (dn) if n is odd
Unlike fftfreq
(but like scipy.fftpack.rfftfreq
)
the Nyquist frequency component is considered to be positive.
Parameters
-
n : int Window length.
-
d : scalar, optional Sample spacing (inverse of the sampling rate). Defaults to 1.
Returns
- f : ndarray
Array of length
n//2 + 1
containing the sample frequencies.
Examples
>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
>>> fourier = np.fft.rfft(signal)
>>> n = signal.size
>>> sample_rate = 100
>>> freq = np.fft.fftfreq(n, d=1./sample_rate)
>>> freq
array([ 0., 10., 20., ..., -30., -20., -10.])
>>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
>>> freq
array([ 0., 10., 20., 30., 40., 50.])
rfftn¶
function rfftn
val rfftn :
?s:int list ->
?axes:int list ->
?norm:string ->
?overwrite_x:bool ->
?workers:int ->
?plan:Py.Object.t ->
x:[>`Ndarray] Np.Obj.t ->
unit ->
Py.Object.t
Compute the N-D discrete Fourier Transform for real input.
This function computes the N-D discrete Fourier Transform over any number of axes in an M-D real array by means of the Fast Fourier Transform (FFT). By default, all axes are transformed, with the real transform performed over the last axis, while the remaining transforms are complex.
Parameters
-
x : array_like Input array, taken to be real.
-
s : sequence of ints, optional Shape (length along each transformed axis) to use from the input. (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). The final element ofs
corresponds ton
forrfft(x, n)
, while for the remaining axes, it corresponds ton
forfft(x, n)
. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. ifs
is not given, the shape of the input along the axes specified byaxes
is used. -
axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last
len(s)
axes are used, or all axes ifs
is also not specified. -
norm : {None, 'ortho'}, optional Normalization mode (see
fft
). Default is None. -
overwrite_x : bool, optional If True, the contents of
x
can be destroyed; the default is False. -
See :func:
fft
for more details. -
workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. -
See :func:
~scipy.fft.fft
for more details. -
plan: object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
.. versionadded:: 1.5.0
Returns
- out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by
axes
, or by a combination ofs
andx
, as explained in the parameters section above. The length of the last axis transformed will bes[-1]//2+1
, while the remaining transformed axes will have lengths according tos
, or unchanged from the input.
Raises
ValueError
If s
and axes
have different length.
IndexError
If an element of axes
is larger than than the number of axes of x
.
See Also
-
irfftn : The inverse of
rfftn
, i.e., the inverse of the N-D FFT of real input. -
fft : The 1-D FFT, with definitions and conventions used.
-
rfft : The 1-D FFT of real input.
-
fftn : The N-D FFT.
-
rfft2 : The 2-D FFT of real input.
Notes
The transform for real input is performed over the last transformation
axis, as by rfft
, then the transform over the remaining axes is
performed as by fftn
. The order of the output is as for rfft
for the
final transformation axis, and as for fftn
for the remaining
transformation axes.
See fft
for details, definitions and conventions used.
Examples
>>> import scipy.fft
>>> x = np.ones((2, 2, 2))
>>> scipy.fft.rfftn(x)
array([[[8.+0.j, 0.+0.j], # may vary
[0.+0.j, 0.+0.j]],
[[0.+0.j, 0.+0.j],
[0.+0.j, 0.+0.j]]])
>>> scipy.fft.rfftn(x, axes=(2, 0))
array([[[4.+0.j, 0.+0.j], # may vary
[4.+0.j, 0.+0.j]],
[[0.+0.j, 0.+0.j],
[0.+0.j, 0.+0.j]]])
set_backend¶
function set_backend
val set_backend :
?coerce:bool ->
?only:bool ->
backend:[`PyObject of Py.Object.t | `Scipy] ->
unit ->
Py.Object.t
Context manager to set the backend within a fixed scope.
Upon entering the with
statement, the given backend will be added to
the list of available backends with the highest priority. Upon exit, the
backend is reset to the state before entering the scope.
Parameters
-
backend: {object, 'scipy'} The backend to use. Can either be a
str
containing the name of a known backend {'scipy'} or an object that implements the uarray protocol. -
coerce: bool, optional Whether to allow expensive conversions for the
x
parameter. e.g., copying a NumPy array to the GPU for a CuPy backend. Impliesonly
. -
only: bool, optional If only is
True
and this backend returnsNotImplemented
, then a BackendNotImplemented error will be raised immediately. Ignoring any lower priority backends.
Examples
>>> import scipy.fft as fft
>>> with fft.set_backend('scipy', only=True):
... fft.fft([1]) # Always calls the scipy implementation
array([1.+0.j])
set_global_backend¶
function set_global_backend
val set_global_backend :
[`PyObject of Py.Object.t | `Scipy] ->
Py.Object.t
Sets the global fft backend
The global backend has higher priority than registered backends, but lower
priority than context-specific backends set with set_backend
.
Parameters
- backend: {object, 'scipy'}
The backend to use.
Can either be a
str
containing the name of a known backend {'scipy'} or an object that implements the uarray protocol.
Raises
- ValueError: If the backend does not implement
numpy.scipy.fft
.
Notes
This will overwrite the previously set global backend, which, by default, is the SciPy implementation.
Examples
We can set the global fft backend:
>>> from scipy.fft import fft, set_global_backend
>>> set_global_backend('scipy') # Sets global backend. 'scipy' is the default backend.
>>> fft([1]) # Calls the global backend
array([1.+0.j])
set_workers¶
function set_workers
val set_workers :
int ->
Py.Object.t
Context manager for the default number of workers used in scipy.fft
Parameters
- workers : int The default number of workers to use
Examples
>>> from scipy import fft, signal
>>> x = np.random.randn(128, 64)
>>> with fft.set_workers(4):
... y = signal.fftconvolve(x, x)
skip_backend¶
function skip_backend
val skip_backend :
[`PyObject of Py.Object.t | `Scipy] ->
Py.Object.t
Context manager to skip a backend within a fixed scope.
Within the context of a with
statement, the given backend will not be
called. This covers backends registered both locally and globally. Upon
exit, the backend will again be considered.
Parameters
- backend: {object, 'scipy'}
The backend to skip.
Can either be a
str
containing the name of a known backend {'scipy'} or an object that implements the uarray protocol.
Examples
>>> import scipy.fft as fft
>>> fft.fft([1]) # Calls default SciPy backend
array([1.+0.j])
>>> with fft.skip_backend('scipy'): # We explicitly skip the SciPy backend
... fft.fft([1]) # leaving no implementation available
Traceback (most recent call last):
...
- BackendNotImplementedError: No selected backends had an implementation ...