fft2

2-D fast Fourier transform

Syntax

Y = fft2(X)

Y = fft2(X,m,n)

Description

Y = fft2(X) returns the two-dimensional Fourier transform of a matrix X using a fast Fourier transform algorithm, which is equivalent to computing fft(fft(X).').'.

When X is a multidimensional array, fft2 computes the 2-D Fourier transform on the first two dimensions of each subarray of X that can be treated as a 2-D matrix for dimensions higher than 2. For example, if X is an m-by-n-by-1-by-2 array, then Y(:,:,1,1) = fft2(X(:,:,1,1)) and Y(:,:,1,2) = fft2(X(:,:,1,2)). The output Y is the same size as X.

Y = fft2(X,m,n) truncates X or pads X with trailing zeros to form an m-by-n matrix before computing the transform. If X is a matrix, then Y is an m-by-n matrix. If X is a multidimensional array, then fft2 shapes the first two dimensions of X according to m and n.

Examples

2-D Transform

The 2-D Fourier transform is useful for processing 2-D signals and other 2-D data such as images.

Create and plot 2-D data with repeated blocks.

P = peaks(20);
X = repmat(P,[5 10]);
imagesc(X)

Compute the 2-D Fourier transform of the data. Shift the zero-frequency component to the center of the output, and plot the resulting 100-by-200 matrix, which is the same size as X.

Y = fft2(X);
imagesc(abs(fftshift(Y)))

Pad X with zeros to compute a 128-by-256 transform.

Y = fft2(X,2^nextpow2(100),2^nextpow2(200));
imagesc(abs(fftshift(Y)));

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 fft2 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

m — Number of transform rows

positive integer scalar

Number of transform rows, specified as a positive integer scalar.

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

n — Number of transform columns

positive integer scalar

Number of transform columns, specified as a positive integer scalar.

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

More About

2-D Fourier Transform

This formula defines the discrete Fourier transform Y of an m-by-n matrix X:

$$Y_{p+1,q+1}={\displaystyle \sum _{j=0}^{m-1}{\displaystyle \sum _{k=0}^{n-1}{\omega }_m^{jp}{\omega }_n^{kq}{X}_{j+1,k+1}}}$$

ω_m and ω_n are complex roots of unity:

$$\begin{array}{l}{\omega }_m=e^{-2\pi i/m}\\ {\omega }_n=e^{-2\pi i/n}\end{array}$$

i is the imaginary unit. p and j are indices that run from 0 to m–1, and q and k are indices that run from 0 to n–1. This formula shifts the indices for X and Y by 1 to reflect matrix indices in MATLAB^®.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• 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™.

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™.

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