Digital Walsh-Fourier spectral conversion for periodic waves

Relationships are presented that allow the determination of Fourier coefficients of frequency-band-limited periodic waves from a truncated spectrum of sequency-aliased Walsh coefficients. The sequency-aliasing compensation matrix takes a simple form when the number of data sample-points is 2^(p+1), where p is a positive integer. For such a case the compensation matrix is a diagonal matrix which premultiplies the converted Fourier coefficients. The sequency-aliasing compensation matrix is combined with Kitai´s matrix (1975, 1978); Kitai´s matrix compensates for truncation of the Walsh series. Kitai´s compensation matrix, which premultiplies Fourier coefficients following conversion into the Fourier domain, takes its simplest form if the highest sequency to be converted is 2^p-1; for this situation, a close relationship exists between the elements of Kitai´s compensation matrix and the sequency-aliasing compensation matrix.