fft

C++ interface for Fast Fourier Transform. More...

array	fft (const array &, int pad=-1)
	Fast Fourier Transform in one dimension. More...
array	fft2 (const array &, int nx=-1, int ny=-1)
	Fast Fourier Transform in two dimensions. More...
array	fft3 (const array &, const dim4 &dims=dim4(0))
	Fast Fourier Transform in three dimensions. More...

Inverse Fast Fourier Transform
array	ifft (const array &, int pad=-1)
	Inverse Fast Fourier Transform in one dimension. More...
array	ifft2 (const array &, int nx=-1, int ny=-1)
	Inverse Fast Fourier Transform in two dimensions. More...
array	ifft3 (const array &, const dim4 &dims=dim4(0))
	Inverse Fast Fourier Transform in three dimensions. More...

Detailed Description

C++ interface for Fast Fourier Transform.

The Fast Fourier Transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) of a signal or array. This is most commonly used to convert data in the time (or space) domain to the frequency domain, Then, the inverse FFT (iFFT) is used to return the data to the original domain.

There are numerous algorithms to compute the FFT of an array, and the specifics of the algorithm depend on the target hardware. Most algorithms, however, use a Cooley-Tukey scheme in a divide-and-conquer approach.

ArrayFire supports up to three-dimensional FFTs. Typically, these multi-dimensional FFTs are implemented using 1D FFTs combined with transpose operations.

array a = randu(4,4);
// a =
//  0.7402        0.9251        0.4702        0.7140
//  0.9210        0.4464        0.5132        0.3585
//  0.0390        0.6673        0.7762        0.6814
//  0.9690        0.1099        0.2948        0.2920

array f = fft(a);
// f =
//  2.6692 +       0.0000i       2.1487 +       0.0000i       2.0544 +       0.0000i       2.0459 +       0.0000i
//  0.7012 +       0.0480i       0.2578 -       0.3364i      -0.3060 -       0.2184i       0.0326 -       0.0665i
// -1.1107 +       0.0000i       1.0362 +       0.0000i       0.4384 +       0.0000i       0.7449 +       0.0000i
//  0.7012 -       0.0480i       0.2578 +       0.3364i      -0.3060 +       0.2184i       0.0326 +       0.0665i

array i = ifft(f);
// i =
//  0.7402 +       0.0000i       0.9251 +       0.0000i       0.4702 +       0.0000i       0.7140 +       0.0000i
//  0.9210 +       0.0000i       0.4464 -       0.0000i       0.5132 -       0.0000i       0.3585 -       0.0000i
//  0.0390 +       0.0000i       0.6673 +       0.0000i       0.7762 +       0.0000i       0.6814 +       0.0000i
//  0.9690 -       0.0000i       0.1099 +       0.0000i       0.2948 +       0.0000i       0.2920 +       0.0000i

Function Documentation

array af::fft	(	const array &	,
		int	pad = -1
	)

Fast Fourier Transform in one dimension.

Applied along each column.

Parameters

[in]

pad

zero-pad or truncate signal to this length before performing transform (default: no change)

Examples:

examples/getting_started/gfor.cpp, and examples/helloworld/helloworld.cpp.

array af::fft2	(	const array &	,
		int	nx = -1,
		int	ny = -1
	)

Fast Fourier Transform in two dimensions.

Applied to first two dimensions in higher dimensional arrays.

Parameters

[in]	nx	Rows are zero-padded or truncated to nx elements before transform (default: no change)
[in]	ny	Columns are zero-padded or truncated to ny elements before transform (default: no change)

Examples:

examples/benchmarks/fft.cpp.

array af::fft3	(	const array &	,
		const dim4 &	dims = dim4(0)
	)

Fast Fourier Transform in three dimensions.

Applied to first three dimensions in higher dimensional arrays.

Parameters

[in]

dims

zero-pad or truncate each dimension before transform

array af::ifft	(	const array &	,
		int	pad = -1
	)

Inverse Fast Fourier Transform in one dimension.

Applied along each column. Normalized (divided) by number of elements.

Parameters

[in]

pad

zero-pad or truncate signal to this length before performing transform (default: no change)

array af::ifft2	(	const array &	,
		int	nx = -1,
		int	ny = -1
	)

Inverse Fast Fourier Transform in two dimensions.

Applied to first two dimensions in higher dimensional arrays. Normalized (divided) by number of elements.

Parameters

[in]	nx	Rows are zero-padded or truncated to nx elements before transform (default: no change)
[in]	ny	Columns are zero-padded or truncated to ny elements before transform (default: no change)

array af::ifft3	(	const array &	,
		const dim4 &	dims = dim4(0)
	)

Inverse Fast Fourier Transform in three dimensions.

Applied to first three dimensions in higher dimensional arrays. Normalize (divide) by number of elements.

Parameters

[in]

dims

zero-pad or truncate each dimension before transform