fftn - N-D fast Fourier transform - MATLAB (original) (raw)

N-D fast Fourier transform

Syntax

Description

Y = fftn([X](#bvhcsbe-1-X)) returns the multidimensional Fourier transform of an N-D array using a fast Fourier transform algorithm. The N-D transform is equivalent to computing the 1-D transform along each dimension of X. The output Y is the same size as X.

example

Y = fftn([X](#bvhcsbe-1-X),[sz](#bvhcsbe-1-sz)) truncates X or pads X with trailing zeros before taking the transform according to the elements of the vector sz. Each element of sz defines the length of the corresponding transform dimensions. For example, if X is a 5-by-5-by-5 array, then Y = fftn(X,[8 8 8]) pads each dimension with zeros resulting in an 8-by-8-by-8 transform Y.

example

Examples

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You can use the fftn function to compute a 1-D fast Fourier transform in each dimension of a multidimensional array.

Create a 3-D signal X. The size of X is 20-by-20-by-20.

x = (1:20)'; y = 1:20; z = reshape(1:20,[1 1 20]); X = cos(2pi0.01x) + sin(2pi0.02y) + cos(2pi0.03*z);

Compute the 3-D Fourier transform of the signal, which is also a 20-by-20-by-20 array.

Pad X with zeros to compute a 32-by-32-by-32 transform.

m = nextpow2(20); Y = fftn(X,[2^m 2^m 2^m]); size(Y)

Input Arguments

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Input array, specified as a matrix or a multidimensional array. If X is of type single, then fftn natively computes in single precision, and Y is also of type single. Otherwise, Y is returned as type double.

Length of the transform dimensions, specified as a vector of positive integers. The elements of sz correspond to the transformation lengths of the corresponding dimensions of X.length(sz) must be at leastndims(X).

More About

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The discrete Fourier transform Y of an _N_-D array X is defined as

Each dimension has length mk for k = 1,2,...,N, and ωmk=e−2πi/mk are complex roots of unity where i is the imaginary unit.

Extended Capabilities

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Usage notes and limitations:

The sz argument must have a fixed size.
For MEX output, MATLAB® Coder™ uses the library that MATLAB uses for FFT algorithms. For standalone C/C++ code, by default, the code generator produces code for FFT algorithms instead of producing FFT library calls. To generate calls to a specific installed FFTW library, provide an FFT library callback class. For more information about an FFT library callback class, see coder.fftw.StandaloneFFTW3Interface (MATLAB Coder).
For simulation of a MATLAB Function block, the simulation software uses the library that MATLAB uses for FFT algorithms. For C/C++ code generation, by default, the code generator produces code for FFT algorithms instead of producing FFT library calls. To generate calls to a specific installed FFTW library, provide an FFT library callback class. For more information about an FFT library callback class, see coder.fftw.StandaloneFFTW3Interface (MATLAB Coder).
Using the Code Replacement Library (CRL), you can generate optimized code that runs on ARM® Cortex®-A processors with Neon extension. To generate this optimized code, you must install theEmbedded Coder® Support Package for ARM Cortex-A Processors (Embedded Coder). The generated code for ARM Cortex-A uses the Ne10 library. For more information, see Ne10 Conditions for MATLAB Functions to Support ARM Cortex-A Processors (Embedded Coder).
Using the Code Replacement Library (CRL), you can generate optimized code that runs on ARM Cortex-M processors. To generate this optimized code, you must install the Embedded Coder Support Package for ARM Cortex-M Processors (Embedded Coder). The generated code for ARM Cortex-M uses the CMSIS library. For more information, see CMSIS Conditions for MATLAB Functions to Support ARM Cortex-M Processors (Embedded Coder).

Usage notes and limitations:

The sz argument must have a fixed size.

The fftn function supports GPU array input with these usage notes and limitations:

The output Y is always complex even if all the imaginary parts are zero.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a