Numerical Exploration of Fourier Transform and Fourier Series

The goal of this book is to offer practical advice to students learning numerical Fourier analysis. Mathematics and engineering students often learn theoretical aspects of the Fourier transform and Fourier series, but then have difficulty knowing how to interpret results of the associated numerical algorithms and calculations. This particular skill has significant value for those who eventually work in some aspect of data analysis, signal processing or signal analysis. Consequently, a text with goals like this one would be attractive.  

 

The authors demonstrate how to obtain frequencies that are present in numerical data, and then use Mathematica to carry out the calculations. Damped, driven oscillators are chosen as an exemplary problem. The authors present numerical solutions, compare them with analytic solutions, and then use the data from the numerical solutions to get the frequency content and the power spectrum of the oscillator.

 

While the plan for the book is admirable, the execution is not. Much of the book consists of page after page of data, plots and computer code.  Verbal exposition and explanation of results are very skimpy and unlikely to help students trying to learn the subject.

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Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.