ABSTRACT
In this chapter, we introduce a way of analyzing=decomposing a continuous-time signal into frequency components given by sinusoidal signals. This process is crucial in the signal processing field since it reveals the frequency content of a signal and simplifies the calculation of a system’s output. This analysis is based on the use of Fourier series. Up to this point, all signals were expressed in the time domain. With the use of the Fourier series, a signal is expressed in the frequency domain and sometimes a frequency representation of a signal reveals more information about the signal than its time domain representation. There are three different and equivalent ways that can be used in order to express a signal into a sum of simple oscillating functions, i.e., into a sum of sines, cosines, or complex exponentials. In this chapter, the symbols n and k are often swapped in order for the code written in the examples to be in accordance with the theoretical mathematical equations.
