# Fourier Series

• Apurba Das
Chapter
Part of the Signals and Communication Technology book series (SCT)

## Abstract

As the readers of communication engineering, we shall look at Fourier series as an efficient tool for signal conditioning. In the world of signals, only sinusoids (and obviously co-sinusoids) are mono-tone signals. If we can successfully express any composite periodic signal into sinusoids, we can directly analyze the components of the signal, i.e., we can obtain the mono tone signal components with definite amount of amplitude (either voltage or current or energy) and phase. This spectral representation can solve a lot of problems in communication engineering like choice of efficient bandwidth for a composite signal transmission. In this chapter, the foundation of Fourier series is discussed with elegant support of mathematics. The applicability of Fourier series and the reasons behind the spectral representation of Fourier spectrum of periodic signals to be discrete, is also discussed. Some interesting worked out problems are presented in this chapter for better understanding of the subject. The visual attacks on the problems are also presented with supporting logics from physical interpretation of Fourier Series. Finally, an application on feature extraction from image using Fourier is discussed.

## Keywords

Fourier Series Fourier Coefficient Periodic Signal Error Energy Trigonometric Fourier Series
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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