Graphical Methods for Evaluating Fourier Integrals

The Fourier transform method of determining the response of a linear system to an arbitrary input signal often has its practical usefulness impaired because of difficulties in evaluating the necessary integrals. One possibility of overcoming these difficulties lies in the application of graphical methods to the transformations. Three such graphical procedures are described, all based upon fundamental properties of the transforms. Each method involves an analysis of the curves of the function to be transformed as a sum of curves of simpler functions whose transforms are known. The methods are useful in cases where the problem is too complicated for a simple analytic solution, or where part of the necessary data is available only in the form of a curve obtained, say, from experimental measurements of transmission characteristics or wave shapes. The accuracy of the methods is restricted only by that of the graphical plotting and curve fitting. If only approximate results are required, they may be obtained relatively quickly by these methods.