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Fourier Analysis and Filtering

Fourier transforms, convolution, digital filtering

Transforms and filters are tools for processing and analyzing discrete data, and are commonly used in signal processing applications and computational mathematics. When data is represented as a function of time or space, the Fourier transform decomposes the data into frequency components. The fft function uses a fast Fourier transform algorithm that reduces its computational cost compared to other direct implementations. For a more detailed introduction to Fourier analysis, see Fourier Transforms. The conv and filter functions are also useful tools for modifying the amplitude or phase of input data using a transfer function.


fft Fast Fourier transform
fft2 2-D fast Fourier transform
fftn N-D fast Fourier transform
fftshift Shift zero-frequency component to center of spectrum
fftw Interface to FFTW library run-time algorithm tuning control
ifft Inverse fast Fourier transform
ifft2 2-D inverse fast Fourier transform
ifftn N-D inverse fast Fourier transform
ifftshift Inverse FFT shift
nextpow2 Exponent of next higher power of 2
conv Convolution and polynomial multiplication
conv2 2-D convolution
convn N-D convolution
deconv Deconvolution and polynomial division
filter 1-D digital filter
filter2 2-D digital filter
ss2tf Convert state-space representation to transfer function


Fourier Transforms

This topic defines the discrete Fourier transform and its implementations, and introduces an example of basic Fourier analysis for signal processing applications.

Basic Spectral Analysis

This topic introduces frequency and power spectrum analysis of two time-domain signals.

Polynomial Interpolation Using FFT

This example shows how to use the fast Fourier transform to estimate coefficients of a polynomial interpolant.

Analyze 2-D Optics with the Fourier Transform

This topic defines the two-dimensional Fourier transform, and uses the fft2 function to transform a 2-D optical mask into frequency space.

Smooth Data with Convolution

This example uses convolution to smooth noisy, two-dimensional data.

Filter Data

This topic defines the filter function in MATLAB®, and presents two examples of filters that modify input data.

Featured Examples

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