Common waveform analysis: a new and practical generalization of Fourier analysis (Q2706547)

Ever since the announcement by Fourier in 1811 of his belief in the possibility of representing a more or less arbitrary function with period \(2\pi\) as the sum of a trigonometric series, and the publication of his book ``Théorie analytique de la chaleur'' in 1822, Fourier analysis has had a profound influence upon a number of developments in Science and Technology. In one of the relatively more modern of sciences, namely Electronics, a signal is often considered as a superposition of ``sine'' and ``cosine'' functions with different frequencies. This book considers the generalization of classical Fourier analysis to frequency analysis based on common waveforms (e.g., sawtooth waves, square waves, triangular waves and trapezoidal waves). The questions considered by the authors are the following.NEWLINENEWLINENEWLINE(i) Can a signal be considered as a superposition of common waveforms with differing frequencies?NEWLINENEWLINENEWLINE(ii) How can a signal be decomposed into a series of common waveforms with differing frequencies?NEWLINENEWLINENEWLINE(iii) How can a signal be best approximated by finite common waveforms?NEWLINENEWLINENEWLINE(iv) How to find a combination of common waveforms that equals a given signal at prescribed points?NEWLINENEWLINENEWLINEThe book is divided into five chapters, with the first chapter introducing some basic concepts, the second and third chapters devoted to square wave, triangular wave and trapezoidal wave analysis, the fourth chapter concentrating on frequency analysis based on generalized periodic functions and the final chapter, the fifth, giving (according to the authors) ``an easy compressed'' version of the monograph. NEWLINENEWLINENEWLINENot withstanding a number of linguistic and typographical errors (The book would have benefitted from some serious editing!) and some tall claims (such as: ``All the unsolved theoretical problems are listed in the book'') on page xi of the Preface, this book might provide a useful addition to the list of references of engineers and mathematicians working in Frequency Analysis/Signalling Theory.