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 |

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

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.

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

This topic defines the `filter`

function
in MATLAB^{®}, and presents two examples of filters that modify input
data.

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