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.

Functions

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 fft Fast Fourier transform fft2 2-D fast Fourier transform fftn N-D fast Fourier transform nufft Nonuniform fast Fourier transform nufftn N-D nonuniform fast Fourier transform fftshift Shift zero-frequency component to center of spectrum fftw Define method for determining FFT algorithm ifft Inverse fast Fourier transform ifft2 2-D inverse fast Fourier transform ifftn Multidimensional inverse fast Fourier transform ifftshift Inverse zero-frequency shift nextpow2 Exponent of next higher power of 2 interpft 1-D interpolation (FFT method)
 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 padecoef Padé approximation of time delays

Topics

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.