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.

example

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.

example

Examples

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2-D Transform

Open Live Script

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)

Figure contains an axes object. The axes object contains an object of type image.

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)))

Figure contains an axes object. The axes object contains an object of type image.

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

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

Figure contains an axes object. The axes object contains an object of type image.

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 fft2 natively computes in single precision, and Y is also of type single. Otherwise, Y is returned as type double.

`m` — Number of transform rows
positive integer scalar

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

`n` — Number of transform columns
positive integer scalar

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

More About

collapse all

2-D Fourier Transform

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

$Y_{p + 1, q + 1} = \sum_{j = 0}^{m - 1} \sum_{k = 0}^{n - 1} ω_{m}^{j p} ω_{n}^{k q} X_{j + 1, k + 1}$

ω_m and ω_n are complex roots of unity:

$\begin{array}{l} ω_{m} = e^{- 2 π i / m} \\ ω_{n} = e^{- 2 π i / n} \end{array}$

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™.

The fft2 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

fft2

Syntax

Description

Examples

2-D Transform

Input Arguments

X — Input array matrix | multidimensional array

m — Number of transform rows positive integer scalar

n — Number of transform columns positive integer scalar

More About

2-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™.

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

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™.

Version History

See Also

`X` — Input array
matrix | multidimensional array

`m` — Number of transform rows
positive integer scalar

`n` — Number of transform columns
positive integer scalar

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

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™.