Walsh-to-Fourier Spectral Conversion for Periodic Waves

Relations are developed for the determination of the Fourier spectra of frequency-limited periodic waves from truncated Walsh spectra. The matrix conversion process is simplest if the highest-order Walsh coefficient in the spectru to be converted is 2n, where n is an integer. For such cases, compensation for truncation consists of a diagonal matrix that premultiplies the Walsh to Fourier conversion matrix and the elements of which are [(sinx)/x]-2 terms. Element values range between unity and less than π2/4. The same compensation matrix is used for determning the Walsh spectra. of sequency-limited waves from 2n Fourier expansion terms. Examples are included which demonstrate the spectral conversion processes, Walsh to Fourier and Fourier to Walsh.