Fourier Series Calculation for Typical Digital Clock Waveforms

Features

• 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 t_r

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

The time domain waveform is plotted for the number of periods specified by the user. The magnitude of the selected number of coefficients |c_n| 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

References

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