Graphical Solutions to Harmonic Analysis

The basic Fourier integral is studied in terms of the maximum possible harmonic amplitudes, whether or not they actually exist. Graphs that define the pulse shapes in terms of time period, pulse width, rise time, and amplitude are produced. Rectangular, trapezoidal, triangular, and two forms of exponential waveshapes are considered. The discrete harmonic concept is further developed to include the harmonic or noise content in a given bandwidth representative of single pulse and step-type functions. Experimental results that demonstrate the accuracy of actual measurements versus the predicted values are included. Very close correlation can be obtained on pulse shapes, which can be represented by the waveforms cited. Additional text that presents the derivation of the graphs and indicates how other waveshapes can similarly be rendered in graphical form is included.