Fourier Series

See: Fourier Analysis, Square Wave, Mathematics, Series (Mathematics), Periodic Function, Sine Wave, Complex Exponential, Discrete-Time Fourier Transform, Z-Transform, Nyquist–Shannon Sampling Theorem.

References

(Wikipedia, 2016) ⇒ http://wikipedia.org/wiki/Fourier_series Retrieved:2016-3-28.
- In mathematics, a Fourier series is a way to represent a (wave-like) 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.