Practical Signals Theory with MATLAB Applications

The Fourier Series

LEARNING OBJECTIVES

By the end of this chapter, the reader will be able to:

• Demonstrate how to express graphically one signal in terms of another
• Explain the concept of orthogonal functions
• List different possible sets of orthogonal functions
• Identify the orthogonal components of an arbitrary signal
• Use MATLAB to combine component signals into a target signal
• Define the orthogonal basis for a Fourier series representation
• Derive the Fourier series components of a periodic signal
• Explain how a Fourier series is affected by time-domain variations
• Apply Fourier series properties to identify a signal from its components
• Use MATLAB to identify the frequency components of a target signal

In this chapter, arbitrary signals are expressed as linear combinations of component signals. Suitable sets of component signals are identified, and the one-sided cosine-frequency approach is extended to represent arbitrary periodic signals as the sum of orthogonal components. This discussion finally leads to the complex Fourier series as a generalized frequency-domain representation of periodic functions.

Chapter Overview

This chapter is divided into three parts. Part One introduces the notion of orthogonal signals and explores the process of identifying the orthogonal components of a signal. There are many possible sets of orthogonal component signals, but in Part Two the use ...