ABSTRACT

This chapter presents the utilities of Walsh functions in analyzing linear time-invariant single-input, single-output systems using a new operational technique. The operational matrix for differentiation cannot be obtained by differentiating Walsh functions as was done by integration in the case of integration matrix because differentiation of Walsh functions gives rise to delta functions and their higher derivatives, which could not be expanded into a Walsh series having a finite number of terms. Corrington formed a table of coefficients for integrating Walsh functions, but he did not realize the potentiality of the table of coefficients as a matrix. In the Walsh domain analysis, since the output response is obtained as a staircase waveform, the method is more or less approximate. However, compared to exact solutions, the results obtained by Walsh method are in good agreement, particularly when 16 or more basis Walsh functions are used.