(Fourier Series)


If we have a fundamental sine wave (1st harmonic) of the following form (for time-domain waves, x may be replaced by ft, where f is the fundamental frequency and t is the time point):

and add nth harmonics of the form:

(where A1 = 1 and B1 = 0 for the fundamental) then the waveform resulting from summing the first N harmonics (including the fundamental) can be expressed as:

We define w to be the limiting case when an infinite number of harmonics are added:


Harmonics (N):

Figure 1: Harmonic sum wN(x) compared to limiting case w(x).

Figure 2: Individual harmonics hn(x) which form wN(x) in figure 1.