Power Electronic Systems: Walsh Analysis with MATLAB
Professor J. L. Walsh. However, he was not the first to propose a complete orthonormal function set that was very much unlike the well-known sine– cosine functions. Precisely, the Walsh functions were piecewise constant in nature as well as bivalued—and hence digital application friendly. Although Walsh functions are so different from the sine–cosine set, they still have some basic similarities with the good old sine–cosine functions. These fundamental properties made Walsh functions to become a strong candidate to application engineers from the mid-1960s.
The proposition of piecewise constant orthonormal function sets was pioneered by Alfred Haar in 1910. Haar function set is now known to be the earliest wavelet function having both scaling and shifting properties. Although each component function in the Haar set is bivalued, its amplitude is different from most of the other members. But in the Walsh set, all the component functions are piecewise constant and switch between two fixed values +1 and −1. This property seemed to be an added advantage for engineering application though the Walsh function set, Haar function set, and block pulse function set are related to one another by similarity transformation.
From the early 1970s, a horde of researchers started working with Walsh functions. They set the ball rolling with the solution of differential as well as integral equations, thus leading to many applications in the area of control theory, including system analysis and identification. Concurrently, the theoretical basis of Walsh analysis has also been strengthened mainly by control engineers and mathematicians. Walsh functions first attracted Anish Deb (the first author) way back in 1982, when he noted the striking similarity between the shapes of different
Walsh functions and different power electronic waveforms, i.e. the output waveforms of chopper, converters, inverters, etc. He initiated the idea of mingling power electronics with Walsh functions and making good use of the advantages offered by this “alternative” piecewise constant function set.
In this book, which is essentially a sort of “marriage” between power electronics and Walsh functions, we have explored many advantages offered by Walsh domain analysis of power electronic systems and have proposed a strong case in its favor to establish its right as an interesting as well as a powerful analysis tool for the study of power electronic systems.
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