Book Series Overview

This book is the third in my music signal processing series, after [422] and [426]. The books in the series can be loosely summarized by the following ``design goals'':

1. Mathematics of the Discrete Fourier Transform
   All about the DFT formula and its constituents, with frequent references to audio applications.

2. Introduction to Digital Filters
   All about ``small'' (mostly first and second order) digital filters used in audio applications, and the elementary concepts of linear systems theory.

3. Physical Audio Signal Processing
   Efficient computational physical models for delay effects and virtual acoustic musical instruments.

4. Spectral Audio Signal Processing
   Analysis, processing, and synthesis of audio signals in terms of spectral representations computed using the Fast Fourier Transform (FFT).

Figure 1 illustrates the dependencies. A solid line indicates a strong dependence, while a dotted line indicates a much weaker (optional) dependence.

Figure 1: Schematic of interdependencies in the music signal processing book series, along with some closely related topics.

The books were originally designed for a two-year course sequence in signal processing applied to music and audio (semester system preferred). The student is expected to pick up elementary physics [169] and programming skills [421,79] elsewhere. In all books, the main chapters contain approximately what is covered in class, while the appendices provide both elementary background material and additional advanced topics.