Section 25.6

Fourier Series (Full)

If a function is neither even nor odd, or defined on , we generally need both sets.

1

Introduction

This is the standard form used in signal processing.

2

Full Formula


Note the change to and limits .

3

Worked Examples

Example 1: Sawtooth Wave

on .

Function is odd.

automatically.

Reduces to Fourier Sine Series (which we solve on with factor 2).

.

Example 2: Shifted Pulse

if , 0 else on .

Neither even nor odd.

(Average is 0.5).

We will have both and terms.

Example 3: Interactive

4

Practice Quiz

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