14.1 INTRODUCTION

The Fourier series technique was developed by the French mathematician Jean Baptiste Joseph Fourier (1768-1830). The Fourier series is a mathematical technique used for analyzing periodic functions by decomposing such a function into a weighted sum of simpler sinusoidal components.

In a simple way we can say, "A Fourier series is an expansion of a periodic function f(t) in terms of an infinite sum of sines and cosines".

14.2 PERIODIC FUNCTIONS

A periodic function is that which repeats itself after regular intervals of time. Mathematically, we can explain a periodic function as

where n is an integer.

By Figure 14.1(a) and Figure 14.1(b) it is clear,

Figure 14.1

Figure 14.1

at

The value of function f(t) is the same after time period "T."

The smallest value of T that satisfies Equation (14.1) is known as the time period.

The functions sin ?t and cos ?t are the most commonly used periodic functions and time period T equals , where ? is known as angular frequency.

14.3 EVEN AND ODD FUNCTIONS

Let there be a function

A function satisfying Equation (14.2) is said to bean even function. For example, cos ?t, , t ², t ⁿ (foreven values of n) are even functions.

Let there be a function

A function satisfying Equation (14.3) is said to be an odd function.

For example, sin ?t, t ⁿ (for odd values of n).

Figure 14.2: Examples of...