Fourier Series Calculation for Typical Digital Clock Waveforms


  • Compute complex Fourier series coefficients (harmonics) of rectangular, triangular or trapezoidal shaped waveform
  • Plot both the time-domain waveform and the magnitude of the coefficients
  • Report numerical values of computed magnitude of the coefficients

Rules and Theories

For a periodic signal x(t) with period T, the Fourier series representation is given by

where is the fundamental angular frequency. The coefficients are defined by

and t1 can be any value. In this applet, t1 = 0 is chosen. An description for the time-domain signal is given for one of the following cases:

(1) Square wave, for a given pulse width

(2) Triangular wave, for a given pulse-width at half-maximum and minimum to maximum rise-time tr

(3) Trapezoidal wave, for a given pulse-width at half-maximum , rise-time tr, falloff-time tf

The time domain waveform is plotted for the number of periods specified by the user. The magnitude of the selected number of coefficients |cn| are plotted. All important numeric values are also reported.

The Applet and User's Guide

  • Choose the appropriate type for the waveform of concern by clicking one of the stubs named "Square", "Triangle" or "Trapezoidal"
  • Set the timing parameters for the chosen type of waveform
  • Set the number of periods to be shown in the time-domain plot
  • Set the number of harmonics needed
  • Click the "Calculate" button


Clayton R. Paul, "Introduction to Electromagnetic Compatibility", John Wiley, New York, 1992, pp.335-377.

Copyright © 2000 - 2011 EE Circle Solutions. All rights reserved.