af_fft

C interface for Fast Fourier Transform. More...

afError	af_fft_S (dim3 dim_O, cfloat *d_O, dim3 dim_I, const float *d_I, unsigned batch, int dim, int direction)
	Single precision, One dimensional fft along dimension. More...
afError	af_fft_C (dim3 dim_O, cfloat *d_O, dim3 dim_I, const cfloat *d_I, unsigned batch, int dim, int direction)
	Complex, Single precision, One dimensional fft along dimension. More...
afError	af_fft_D (dim3 dim_O, cdouble *d_O, dim3 dim_I, const double *d_I, unsigned batch, int dim, int direction)
	Double precision, One dimensional fft along dimension. More...
afError	af_fft_Z (dim3 dim_O, cdouble *d_O, dim3 dim_I, const cdouble *d_I, unsigned batch, int dim, int direction)
	Complex, Double precision, One dimensional fft along dimension. More...
afError	af_fft2_S (unsigned xo, unsigned yo, cfloat *d_O, unsigned xi, unsigned yi, const float *d_I, unsigned batch, int direction)
	Single precision, two dimensional fft. More...
afError	af_fft2_C (unsigned xo, unsigned yo, cfloat *d_O, unsigned xi, unsigned yi, const cfloat *d_I, unsigned batch, int direction)
	Complex, Single precision, two dimensional fft. More...
afError	af_fft2_D (unsigned xo, unsigned yo, cdouble *d_O, unsigned xi, unsigned yi, const double *d_I, unsigned batch, int direction)
	Double precision, two dimensional fft. More...
afError	af_fft2_Z (unsigned xo, unsigned yo, cdouble *d_O, unsigned xi, unsigned yi, const cdouble *d_I, unsigned batch, int direction)
	Complex, Double precision, two dimensional fft. More...
afError	af_fft3_S (dim3 dims_O, cfloat *d_O, dim3 dims_I, const float *d_I, unsigned batch, int direction)
	Single precision, multi-dimensional fft. More...
afError	af_fft3_C (dim3 dims_O, cfloat *d_O, dim3 dims_I, const cfloat *d_I, unsigned batch, int direction)
	Complex, Single precision, multi-dimensional fft. More...
afError	af_fft3_D (dim3 dims_O, cdouble *d_O, dim3 dims_I, const double *d_I, unsigned batch, int direction)
	Double precision, multi-dimensional fft. More...
afError	af_fft3_Z (dim3 dims_O, cdouble *d_O, dim3 dims_I, const cdouble *d_I, unsigned batch, int direction)
	Complex, Double precision, multi-dimensional fft. 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

afError af_fft_S	(	dim3	dim_O,
		cfloat *	d_O,
		dim3	dim_I,
		const float *	d_I,
		unsigned	batch,
		int	dim,
		int	direction
	)

Single precision, One dimensional fft along dimension.

Parameters

[in]	dim_O	Dimensions of the output array
[out]	d_O	Output array (always complex)
[in]	dim_I	Dimensions of the input array
[in]	d_I	Input array
[in]	batch	Number of input tiles
[in]	dim	Dimension along which result is computed (0 along column, 1 along row)
[in]	direction	Direction of transform: -1 for forward, 1 for backward (inverse)

afError af_fft_C	(	dim3	dim_O,
		cfloat *	d_O,
		dim3	dim_I,
		const cfloat *	d_I,
		unsigned	batch,
		int	dim,
		int	direction
	)

Complex, Single precision, One dimensional fft along dimension.

afError af_fft_D	(	dim3	dim_O,
		cdouble *	d_O,
		dim3	dim_I,
		const double *	d_I,
		unsigned	batch,
		int	dim,
		int	direction
	)

Double precision, One dimensional fft along dimension.

afError af_fft_Z	(	dim3	dim_O,
		cdouble *	d_O,
		dim3	dim_I,
		const cdouble *	d_I,
		unsigned	batch,
		int	dim,
		int	direction
	)

Complex, Double precision, One dimensional fft along dimension.

afError af_fft2_S	(	unsigned	xo,
		unsigned	yo,
		cfloat *	d_O,
		unsigned	xi,
		unsigned	yi,
		const float *	d_I,
		unsigned	batch,
		int	direction
	)

Single precision, two dimensional fft.

Parameters

[in]	xo	number of rows in the output
[in]	yo	number of columns in the output
[out]	d_O	Output array (always complex)
[in]	xi	number of rows in the input
[in]	yi	number of columns in the output
[in]	d_I	Input array
[in]	batch	Number of input tiles
[in]	direction	Direction of transform: -1 for forward, 1 for backward (inverse)

afError af_fft2_C	(	unsigned	xo,
		unsigned	yo,
		cfloat *	d_O,
		unsigned	xi,
		unsigned	yi,
		const cfloat *	d_I,
		unsigned	batch,
		int	direction
	)

Complex, Single precision, two dimensional fft.

afError af_fft2_D	(	unsigned	xo,
		unsigned	yo,
		cdouble *	d_O,
		unsigned	xi,
		unsigned	yi,
		const double *	d_I,
		unsigned	batch,
		int	direction
	)

Double precision, two dimensional fft.

afError af_fft2_Z	(	unsigned	xo,
		unsigned	yo,
		cdouble *	d_O,
		unsigned	xi,
		unsigned	yi,
		const cdouble *	d_I,
		unsigned	batch,
		int	direction
	)

Complex, Double precision, two dimensional fft.

afError af_fft3_S	(	dim3	dims_O,
		cfloat *	d_O,
		dim3	dims_I,
		const float *	d_I,
		unsigned	batch,
		int	direction
	)

Single precision, multi-dimensional fft.

Parameters

[in]	dims_O	Dimensions of the output array
[out]	d_O	Output array (always complex)
[in]	dims_I	Dimensions of the input array
[in]	d_I	Input array
[in]	batch	Number of input tiles
[in]	direction	Direction of transform: -1 for forward, 1 for backward (inverse)

afError af_fft3_C	(	dim3	dims_O,
		cfloat *	d_O,
		dim3	dims_I,
		const cfloat *	d_I,
		unsigned	batch,
		int	direction
	)

Complex, Single precision, multi-dimensional fft.

afError af_fft3_D	(	dim3	dims_O,
		cdouble *	d_O,
		dim3	dims_I,
		const double *	d_I,
		unsigned	batch,
		int	direction
	)

Double precision, multi-dimensional fft.

afError af_fft3_Z	(	dim3	dims_O,
		cdouble *	d_O,
		dim3	dims_I,
		const cdouble *	d_I,
		unsigned	batch,
		int	direction
	)

Complex, Double precision, multi-dimensional fft.