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.

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

3-D Transform

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

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.

Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical
Complex Number Support: Yes

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).

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical

More About

N-D Fourier Transform

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

$$Y_{p_1,p_2,\mathrm{...},p_N}={\displaystyle \sum _{j_1=0}^{m_1-1}{\omega }_{m_1}^{p_1{j}_1}{\displaystyle \sum _{j_2=0}^{m_2-1}{\omega }_{m_2}^{p_2{j}_2}\mathrm{...}{\displaystyle \sum _{j_N}^{m_N-1}{\omega }_{m_N}^{p_N{j}_N}{X}_{j_1,j_2,\mathrm{...},j_N}}}.}$$

Each dimension has length m_k for k = 1,2,...,N, and $${\omega }_{m_k}=e^{-2\pi i/m_k}$$ 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). 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).

GPU Code Generation

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

Usage notes and limitations:

• The sz argument must have a fixed size.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

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

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).

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).

Version History

Introduced before R2006a