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A True Adventure
on September 29, 2001
The motivation for this book is rooted in a club in Japan that is dedicated to learning foreign languages. Its members began to wonder about the sounds of languages, and this curiosity led them to the study of Fourier series, which they applied to analyze spoken sounds.
To start with, this book introduces the concepts behind the Fourier series and the calculation of Fourier coefficients. It then discusses Fourier analysis of the five vowels of the Japanese language. The conclusions are enlightening to say the least.
Rather than end here, as it could have, this book continues on to develop in some detail the mathematics behind the Fourier series. This includes forays into trigonometry, limits, differentiaion, integration, vectors, infinite series, the constants e and i, and Euler's formula. At all times it provides concrete motivation for new concepts, and supports them with superb visualization. When previously introduced concepts are needed, they are always reviewed in place, instead of assuming that the reader has mastered them, or will go back to the original material.
One strength of this book that should not be overlooked is that its translation is very good. That is, the reader is not aware that it is a translation.
While most people who are aware of Fourier series probably have the necessary background in mathematics to make this book feel "accessible", I wonder whether someone who has never gone beyond high school algebra and geometry would feel the same way.
One disappointment for me was the final chapter, the one on FFT. Its presentation of the discrete Fourier transform was good, but its development of the algorithm became unnecesarrily complicated. Though I found the explanation in an algorithms book more to my liking, without the background from this book, particularly Euler's formula, I surely would not have understood that one at all.