# 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.

## Funzioni

espandi tutto

 `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

## Argomenti

• 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.