# Chapter 22--Fourier Series: Fundamental Period, Frequency, and Angular Frequency

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## Contents

## Period, Frequency, and Angular Frequency

### Period

Long long ago, in a high school class called trigonometry, we leaned about **periodic functions**. A periodic function is a function that repeats itself over and over for infinity. The **period** of the function is the distance of one iteration that is infinitely repeating.

*t*,

Where T is the period

The picture to the right shows the plot of the standard sine function whose period is . What the plot does not show is that the line keeps extending and repeating the bumps and valleys over the whole x axis, or . But wait! Can't the period also be or ? In fact it can. Because the graph of sin(x) repeats itself every units, the period of the function is actually where n is any whole number from zero to

### Frequency and Angular Frequency

The **Frequency** is the number of periods per second and is defined mathematically as

The standard unit of measurement for frequency is Hz (Hertz). 1 Hz = 1 cycle/second

The **Angular Frequency** is defined as

The standard unit of measurement for angular frequency is in radians/second.

### Fundamental Period, Frequency, and Angular Frequency

The **fundamental period** is the smallest positive real number for which the periodic equation holds true.

The **fundamental frequency** is defined as .

The **fundamental angular frequency** is defined as .

## References

## Author

Andrew Roth