fftn

N-D fast Fourier transform

Syntax

Y = fftn(X)

Y = fftn(X,sz)

Description

Y = fftn(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,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.

Examples

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3-D Transform

Open Live Script

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(2*pi*0.01*x) + sin(2*pi*0.02*y) + cos(2*pi*0.03*z);

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

Y = fftn(X);

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)

ans = 1×3

    32    32    32

Input Arguments

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`X` — Input array
matrix | multidimensional array

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.

`sz` — Length of transform dimensions
vector of positive integers

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 least ndims(X).

More About

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N-D Fourier Transform

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

$Y_{p_{1}, p_{2}, ..., p_{N}} = \sum_{j_{1} = 0}^{m_{1} - 1} ω_{m_{1}}^{p_{1} j_{1}} \sum_{j_{2} = 0}^{m_{2} - 1} ω_{m_{2}}^{p_{2} j_{2}} ... \sum_{j_{N}}^{m_{N} - 1} ω_{m_{N}}^{p_{N} j_{N}} X_{j_{1}, j_{2}, ..., j_{N}} .$

Each dimension has length m_k for k = 1,2,...,N, and $ω_{m_{k}} = e^{- 2 π i / m_{k}}$ are complex roots of unity where i is the imaginary unit.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

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 the Embedded Coder^® Support Package for ARM Cortex-A Processors (Embedded Coder Support Package for ARM Cortex-A Processors). 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 Support Package for ARM Cortex-A Processors).
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 Support Package for ARM Cortex-M Processors). 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 Support Package for ARM Cortex-M Processors).

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

The sz argument must have a fixed size.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

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).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Documentation

fftn

Syntax

Description

Examples

3-D Transform

Input Arguments

`X` — Input array
matrix | multidimensional array

`sz` — Length of transform dimensions
vector of positive integers

More About

N-D Fourier Transform

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

See Also

MATLAB Documentation

Support

Documentation

fftn

Syntax

Description

Examples

3-D Transform

Input Arguments

X — Input array matrix | multidimensional array

sz — Length of transform dimensions vector of positive integers

More About

N-D Fourier Transform

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

See Also

MATLAB Documentation

Support

`X` — Input array
matrix | multidimensional array

`sz` — Length of transform dimensions
vector of positive integers

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.