Fourier Series - Math Terms & Solutions - Maplesoft

# Fourier Series

Maple makes it easy to calculate Fourier series and other series representations.

# What is the Fourier Series?

In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves. More formally, it decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or, equivalently, complex exponentials). The discrete-time Fourier transform is a periodic function, often defined in terms of a Fourier series. The Z-transform, another example of application, reduces to a Fourier series for the important case |z|=1. Fourier series are also central to the original proof of the Nyquist-Shannon sampling theorem. The study of Fourier series is a branch of Fourier analysis.1

Maple is powerful math software that makes it easy to calculate Fourier series, and to analyze, explore, visualize, and solve mathematical problems from virtually every branch of mathematics. Student pricing available.

## Fourier Series: Applications and Resources

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1 Source: Wikipedia