FFT Transforms

All FFT functions are accessed via the np.fft namespace and return complex128 arrays. numpy-ts uses a Cooley-Tukey radix-2 algorithm for power-of-2 sizes and Bluestein’s algorithm for arbitrary sizes.

fft

Compute the 1-D discrete Fourier Transform.

function fft(
  a: ArrayLike,
  n?: number,
  axis?: number,
  norm?: 'backward' | 'ortho' | 'forward'
): NDArray

Name	Type	Default	Description
`a`	`ArrayLike`	—	Input array (real or complex).
`n`	`number`	`a.shape[axis]`	Length of the transformed axis. If shorter than the input, the input is truncated. If longer, it is zero-padded.
`axis`	`number`	`-1`	Axis along which to compute the FFT.
`norm`	`'backward' \| 'ortho' \| 'forward'`	`'backward'`	Normalization mode. `'backward'` applies no scaling on forward, `1/n` on inverse. `'ortho'` applies `1/sqrt(n)` to both. `'forward'` applies `1/n` on forward.

Returns: NDArray — Complex128 array containing the FFT result.

import * as np from 'numpy-ts';

const signal = np.array([1, 2, 3, 4]);
const spectrum = np.fft.fft(signal);
// array([10+0j, -2+2j, -2+0j, -2-2j])

ifft

Compute the 1-D inverse discrete Fourier Transform.

function ifft(
  a: ArrayLike,
  n?: number,
  axis?: number,
  norm?: 'backward' | 'ortho' | 'forward'
): NDArray

Name	Type	Default	Description
`a`	`ArrayLike`	—	Input array (typically complex, from `fft`).
`n`	`number`	`a.shape[axis]`	Length of the transformed axis.
`axis`	`number`	`-1`	Axis along which to compute the IFFT.
`norm`	`'backward' \| 'ortho' \| 'forward'`	`'backward'`	Normalization mode.

Returns: NDArray — Complex128 array containing the IFFT result.

import * as np from 'numpy-ts';

const signal = np.array([1, 2, 3, 4]);
const spectrum = np.fft.fft(signal);
const recovered = np.fft.ifft(spectrum);
// array([1+0j, 2+0j, 3+0j, 4+0j])

fft2

Compute the 2-D discrete Fourier Transform. Equivalent to applying fft along the last two axes.

function fft2(
  a: ArrayLike,
  s?: [number, number],
  axes?: [number, number],
  norm?: 'backward' | 'ortho' | 'forward'
): NDArray

Name	Type	Default	Description
`a`	`ArrayLike`	—	Input array (at least 2-D).
`s`	`[number, number]`	shape of `a` along `axes`	Shape of the output along the transform axes. Zero-pads or truncates as needed.
`axes`	`[number, number]`	`[-2, -1]`	Axes over which to compute the 2-D FFT.
`norm`	`'backward' \| 'ortho' \| 'forward'`	`'backward'`	Normalization mode.

Returns: NDArray — Complex128 array containing the 2-D FFT result.

import * as np from 'numpy-ts';

const a = np.array([[1, 2], [3, 4]]);
const F = np.fft.fft2(a);
// 2-D complex spectrum

ifft2

Compute the 2-D inverse discrete Fourier Transform.

function ifft2(
  a: ArrayLike,
  s?: [number, number],
  axes?: [number, number],
  norm?: 'backward' | 'ortho' | 'forward'
): NDArray

Name	Type	Default	Description
`a`	`ArrayLike`	—	Input array (complex, from `fft2`).
`s`	`[number, number]`	shape of `a` along `axes`	Shape of the output along the transform axes.
`axes`	`[number, number]`	`[-2, -1]`	Axes over which to compute the 2-D IFFT.
`norm`	`'backward' \| 'ortho' \| 'forward'`	`'backward'`	Normalization mode.

Returns: NDArray — Complex128 array containing the 2-D IFFT result.

fftn

Compute the N-dimensional discrete Fourier Transform.

function fftn(
  a: ArrayLike,
  s?: number[],
  axes?: number[],
  norm?: 'backward' | 'ortho' | 'forward'
): NDArray

Name	Type	Default	Description
`a`	`ArrayLike`	—	Input array.
`s`	`number[]`	shape of `a` along `axes`	Shape of the output along the transform axes.
`axes`	`number[]`	all axes	Axes over which to compute the FFT.
`norm`	`'backward' \| 'ortho' \| 'forward'`	`'backward'`	Normalization mode.

Returns: NDArray — Complex128 array containing the N-D FFT result.

import * as np from 'numpy-ts';

const a = np.zeros([4, 4, 4]);
const F = np.fft.fftn(a);

ifftn

Compute the N-dimensional inverse discrete Fourier Transform.

function ifftn(
  a: ArrayLike,
  s?: number[],
  axes?: number[],
  norm?: 'backward' | 'ortho' | 'forward'
): NDArray

Name	Type	Default	Description
`a`	`ArrayLike`	—	Input array (complex, from `fftn`).
`s`	`number[]`	shape of `a` along `axes`	Shape of the output along the transform axes.
`axes`	`number[]`	all axes	Axes over which to compute the IFFT.
`norm`	`'backward' \| 'ortho' \| 'forward'`	`'backward'`	Normalization mode.

Returns: NDArray — Complex128 array containing the N-D IFFT result.

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Utilities

fft

ifft

fft2

ifft2

fftn

ifftn

​fft

​ifft

​fft2

​ifft2

​fftn

​ifftn

fft

ifft

fft2

ifft2

fftn

ifftn