fourier¶

Fourier series models¶

The Fourier series is a sum of sine and cosine functions that describes a periodic signal, and can be represented in trigonometric form as

\[y=a_0+\sum_{k=1}^na_k\cos{(k\omega x)}+b_k\sin{(k\omega x)}\]

where \(a_0\) models a constant (intercept) term in the data and is associated with the \(k=0\) cosine term, \(\omega\) is the fundamental frequency of the signal, and \(n\) is the number of terms (harmonics) in the series.

This module provides the general Fourier series model above for any number of terms \(k\), as well as convenience functions for Fourier series models with \(1\leq k\leq 8\) analogous to MATLAB’s fourier1, fourier2, etc.

Functions

`fourier`	General Fourier series model.
`fourier1`	Convenience function for the `fourier1` model from MATLAB.
`fourier2`	Convenience function for the `fourier2` model from MATLAB.
`fourier3`	Convenience function for the `fourier3` model from MATLAB.
`fourier4`	Convenience function for the `fourier4` model from MATLAB.
`fourier5`	Convenience function for the `fourier5` model from MATLAB.
`fourier6`	Convenience function for the `fourier6` model from MATLAB.
`fourier7`	Convenience function for the `fourier7` model from MATLAB.
`fourier8`	Convenience function for the `fourier8` model from MATLAB.