Introduction to Digital Filters: with Audio Applications Review

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(More customer reviews)I've got to hand it to two particular authors for bringing the subject of digital filters to musicians and the subject of music to engineers and computer scientists - Perry Cook and the author of this book, Julius O. Smith. Until recently only Mr. Cook's books have been in print. Mr. Smith's books have been purely in the online realm unless you are an actual student of his. Now two of his online publications are available for those of us interested in the practical details of musical signal processing. There is this book, of course, and also the excellent "Mathematics of the Discrete Fourier Transform".
I've already read the two books in print - and skimmed through the dozens more Mr. Smith has on his website. The online access gives you a good idea of whether or not you want to purchase these books, but to get access to the problem sets you need the print version of the book. For the low price compared to other signal processing books, believe me it's worth it. By working through both the math and the practical applications of filter design in processing audio, the author gives the reader a real intuition for the subject. You might want to have Oppenheim and Schafer's book on the subject, "Discrete Time Signal Processing", on hand for the rigorous mathematics part of signal processing. Keep this one on hand if you want to see signal processing in action and explained carefully. I find both books to be essential depending on what I'm doing. The following is a list of topics covered in the book:
The Simplest Lowpass Filter
Matlab Filter Analysis
Analysis of A Digital Comb Filter
Linear Time-Invariant FIlters
Time Domain Representations
Transfer Function Analysis
Frequency Response Analysis
Pole-Zero Analysis
Implementation Structures
Filters Preserving Phase
Minimum Phase Filters
Background Fundamentals
Elementary Audio Digital Filters
Allpass Filters
Laplace Transform Analysis
Analog Filters
Matrix Filter Representations
State Space Filters
Linear Time Varying Filters
Recursive Digital Filter Design
Matlab Utilities
Digital Filtering in Faust and Pure Data (PD)
To find Julius Smith's online publications just type "Julius O. Smith" into Google. That will take you to his homepage and from there you can easily find his many online publications, including most of this book.

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A digital filter can be pictured as a "black box" that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds. For example, digital filters are used to implement graphic equalizers and other digital audio effects.This book is a gentle introduction to digital filters, including mathematical theory, illustrative examples, some audio applications, and useful software starting points. The theory treatment begins at the high-school level, and covers fundamental concepts in linear systems theory and digital filter analysis. Various "small" digital filters are analyzed as examples, particularly those commonly used in audio applications. Matlab programming examples are emphasized for illustrating the use and development of digital filters in practice.

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