Mathematics

Fourier Analysis and the Fast Fourier Transform (FFT)

Fourier analysis is extremely useful for data analysis, as it breaks down a signal into constituent sinusoids of different frequencies. For sampled vector data, Fourier analysis is performed using the discrete Fourier transform (DFT).

The fast Fourier transform (FFT) is an efficient algorithm for computing the DFT of a sequence; it is not a separate transform. It is particularly useful in areas such as signal and image processing, where its uses range from filtering, convolution, and frequency analysis to power spectrum estimation.

This section:

• Summarizes the Fourier transform functions
• Introduces Fourier transform analysis with an example about sunspot activity
• Calculates magnitude and phase of transformed data
• Discusses the dependence of execution time on length of the transform

Difference Equations and Filtering

Function Summary