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Walsh-to-Fourier Spectral Conversion for Periodic Waves

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1 Author(s)
Kitai, Reuven ; Department of Electrical Engineering, McMaster University, Hamilton, Ont., Canada

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 ¿2/4. 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.

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Electromagnetic Compatibility, IEEE Transactions on  (Volume:EMC-17 ,  Issue: 4 )