This book is the third in my music signal processing series, after [454] and [452]. The books can be loosely summarized by the following ``design goals'':

**MATHEMATICS OF THE DISCRETE FOURIER TRANSFORM**

All about the DFT formula and its constituents, with frequent references to audio applications.**INTRODUCTION TO DIGITAL FILTERS**

A gentle introduction to the analysis and implementation of digital filters, with particular emphasis on audio applications.**PHYSICAL AUDIO SIGNAL PROCESSING**

Efficient computational physical models for delay effects and virtual acoustic musical instruments.**SPECTRAL AUDIO SIGNAL PROCESSING**

Analysis, processing, and synthesis of audio signals in terms of spectral representations computed using a Fast Fourier Transform (FFT).

Figure 1 illustrates the dependencies. A solid line indicates a strong dependence, while a dotted line indicates a weaker (optional) dependence. The student is expected to pick up elementary physics [181] and programming skills [446,86] 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.

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