For each of the signals below solve for the Fourier Series A

For each of the signals below, solve for the Fourier Series A_n and then use Matlab to verify your solution. Note that for signal x_4(t), the signal is equal to e^t on the interval 0

Solution

In mathematics, a Fourier series (English pronunciation: /frie/) 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). Thediscrete-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.