Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 9. Overview of Fourier Analysis

Fourier analysis is based on the notion that signals can be represented and analyzed as weighted sums of sinusoidal components over a range of different frequencies. The collection of amplitudes and phases for the sinusoids needed to completely represent the signal is usually called the spectrum of the signal. Depending upon the nature of the signal being analyzed, the spectrum can span either a continuum of frequencies or a countable (but possibly infinite) set of discrete frequencies.

9.1. Fourier Series

Periodic continuous-time signals have finite power (but infinite energy), and can be analyzed using the Fourier series (FS) defined by

for n = 0, ±1, ±2, ±3, . . ., ±∞

where ω₀ is the fundamental radian ...