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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.

Sample data plotted in the time or space domain and the Fourier transform of the data plotted in the frequency domain


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fftFast Fourier transform
fft22-D fast Fourier transform
fftnN-D fast Fourier transform
nufftNonuniform fast Fourier transform (Since R2020a)
nufftnN-D nonuniform fast Fourier transform (Since R2020a)
fftshiftShift zero-frequency component to center of spectrum
fftwDefine method for determining FFT algorithm
ifftInverse fast Fourier transform
ifft22-D inverse fast Fourier transform
ifftnMultidimensional inverse fast Fourier transform
ifftshiftInverse zero-frequency shift
nextpow2Exponent of next higher power of 2
interpft1-D interpolation (FFT method)
convConvolution and polynomial multiplication
conv22-D convolution
convnN-D convolution
deconvLeast-squares deconvolution and polynomial division
filter1-D digital filter
filter22-D digital filter
ss2tfConvert state-space representation to transfer function
padecoefPadé approximation of time delays


  • Fourier Transforms

    The Fourier transform is a powerful tool for analyzing data across many applications, including Fourier analysis for signal processing.

  • Basic Spectral Analysis

    Use the Fourier transform for frequency and power spectrum analysis of time-domain signals.

  • 2-D Fourier Transforms

    Transform 2-D optical data into frequency space.

  • Smooth Data with Convolution

    Smooth noisy, 2-D data using convolution.

  • Filter Data

    Filtering is a data processing technique used for smoothing data or modifying specific data characteristics, such as signal amplitude.