TABLE OF CONTENTS This chapter is an introduction to Fourier series. We begin with the definition of sinusoids that are harmonically related and the procedure for determining the coefficients of the trigonometric form of the series. Then, we discuss the different types of symmetry and how they can be used to predict the terms that may be present. Several examples are presented to illustrate the approach. The alternate trigonometric and the exponential forms are also presented.
The French mathematician Fourier found that any periodic waveform, that is, a waveform that repeats itself after some time, can be expressed as a series of harmonically related sinusoids, i.e., sinusoids whose frequences are multiples of a fundamental frequency (or first harmonic). For example, a series of sinusoids with frequencies 1 MHz, 2 MHz, 3 MHz, and so on, contains the fundamental frequency of 1 MHz, a second harmonic of 2 MHz, a third harmonic of 3 MHz, and so on. In general, any periodic waveform f(t) can be expressed as
or
where the first term a 0/2 is a constant, and represents the DC (average) component of f(t). Thus, if f(t) represents some voltage v(t), or current i(t), the term a 0/2 is the average value of v(t) or i(t).
The terms with the coefficients a 1 and b 1 together, represent the fundamental frequency component ? [*]. Likewise, the terms with the coefficients a 2 and b 2 together, represent the second harmonic...
