mindspore.ops.FFTWithSize

class mindspore.ops.FFTWithSize(signal_ndim, inverse, real, norm='backward', onesided=True, signal_sizes=())[source]

Fourier transform, can be adjusted by parameters to achieve FFT/IFFT/RFFT/IRFFT.

For fft, it computes the following expression:

\[X[\omega_1, \dots, \omega_d] = \sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d] e^{-j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},\]

where \(d\) = signal_ndim is number of dimensions for the signal, and \(N_i\) is the size of signal dimension \(i\).

For ifft, it computes the following expression:

\[X[\omega_1, \dots, \omega_d] = \frac{1}{\prod_{i=1}^d N_i} \sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d] e^{\ j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},\]

where \(d\) = signal_ndim is number of dimensions for the signal, and \(N_i\) is the size of signal dimension \(i\).

Note

FFT/IFFT requires complex64 or complex128 inputs, return complex64 or complex128 outputs.
RFFT requires bool, uint8, int8, int16, int32, int64, float32 and float64 inputs, return complex64 or complex128 outputs.
IRFFT requires complex64 or complex128 inputs, return float32 or float64 outputs.

Warning

This is an experimental API that is subject to change or deletion.

Parameters

signal_ndim (int) – The number of dimensions in each signal, this controls how many dimensions of the fourier transform are realized, can only be 1, 2 or 3.
inverse (bool) –
Whether it is the inverse transformation, used to select from FFT and RFFT or IFFT and IRFFT.
- when set to True: IFFT and IRFFT.
- when set to False: FFT and RFFT.
real (bool) –
Whether it is the real transformation, combines with inverse to select a specific transformation mode:
- inverse is False , real is False : corresponds to FFT.
- inverse is True , real is False : corresponds to IFFT.
- inverse is False , real is True : corresponds to RFFT.
- inverse is True , real is True : corresponds to IRFFT.
norm (str, optional) –
The normalization, optional values: [ "backward" , "forward" , "ortho" ]. Default value: "backward" .
- "backward" has the direct transforms unscaled and the inverse transforms scaled by \(1/n\), where n is the input x’s element numbers.
- "ortho" has both direct and inverse transforms are scaled by \(1/\sqrt n\).
- "forward" has the direct transforms scaled by \(1/n\) and the inverse transforms unscaled.
onesided (bool, optional) – Controls whether the input is halved to avoid redundancy. Default: True .
signal_sizes (tuple, optional) –
Size of the original signal (the signal before rfft, no batch dimension), only in IRFFT mode and set onesided to True requires the parameter, the following conditions must be satisfied. Default: () .
- The length of signal_sizes is equal to the signal_ndim of the IRFFT: \(len(signal_sizes)=signal_ndim\).
- The last dimension of signal_sizes divided by 2 is equal to the last dimension of the IRFFT input: \(signal_size[-1]/2+1=x.shape[-1]\).
- signal_sizes has exactly the same dimensions as the input shape except for the last dimension: \(signal_sizes[:-1]=x.shape[:-1]\).

Inputs:

x (Tensor) - The dimension of the input tensor must be greater than or equal to signal_ndim.

Outputs:

A tensor containing the complex-to-complex, real-to-complex or complex-to-real Fourier transform result.

Raises

TypeError – If the input type of FFT/IFFT/IRFFT is not one of: complex64, complex128.
TypeError – If the input type is not Tensor.
ValueError – If x dimension is less than signal_ndim.
ValueError – If signal_ndim is greater than 3 or less than 1.
ValueError – If norm is none of “backward”, “forward” or “ortho”.

Supported Platforms:: Ascend GPU CPU

Examples

>>> import mindspore
>>> import numpy as np
>>> from mindspore import Tensor, ops
>>> # case FFT: signal_ndim: 1, inverse: False, real: False.
>>> fft_in = Tensor(np.array([2, 1, 2]), mindspore.complex64)
>>> fft_net = ops.FFTWithSize(signal_ndim=1, inverse=False, real=False)
>>> fft_output = fft_net(fft_in)
>>> print(fft_output)
[5.        +0.j         0.5       +0.86602545j 0.50000006-0.8660255j ]
>>> # case IFFT: signal_ndim: 1, inverse: True, real: False.
>>> ifft_in = fft_output
>>> ifft_net = ops.FFTWithSize(signal_ndim=1, inverse=True, real=False)
>>> ifft_output = ifft_net(ifft_in)
>>> print(ifft_output)
[2.        -1.9868216e-08j 0.99999994+0.0000000e+00j
 1.9999999 +7.9472862e-08j]
>>> # case RFFT2D: signal_ndim: 2, inverse: False, real: True.
>>> rfft_in = Tensor(np.array([[2, 1, 2], [3, 1, 6]]), mindspore.float32)
>>> rfft_net = ops.FFTWithSize(signal_ndim=2, inverse=False, real=True)
>>> rfft_output = rfft_net(rfft_in)
>>> print(rfft_output)
[[ 1.5000000e+01+1.1920929e-07j -2.3841858e-07+5.1961522e+00j]
 [-5.0000000e+00-2.9802322e-08j  9.9999988e-01-3.4641016e+00j]]
>>> # case IRFFT2D: signal_ndim: 2, inverse: True, real: True.
>>> irfft_in = rfft_output
>>> irfft_net = ops.FFTWithSize(signal_ndim=2, inverse=True, real=True, signal_sizes=rfft_in.shape)
>>> irfft_output = irfft_net(irfft_in)
>>> print(irfft_output)
[[2.         1.         2.        ]
 [3.         0.99999994 5.9999995 ]]