Introduction to Digital Filters: with Audio Applications

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.

Julius O. Smith is a research engineer and musician devoted to developing new technologies for music. He received the B.S.E.E. degree from Rice University, Houston, TX, in 1975 (Control, Circuits, and Communication). He received the M.S. and Ph.D. degrees in E.E. from Stanford University, Stanford, CA, in 1978 and 1983, respectively. His Ph.D. research was devoted to improved methods for digital filter design and system identification applied to music and audio systems. From 1975 to 1977 he worked in the Signal Processing Department at ESL, Sunnyvale, CA, on systems for digital communications. From 1982 to 1986 he was with the Adaptive Systems Department at Systems Control Technology, Palo Alto, CA, where he worked in the areas of adaptive filtering and spectral estimation. From 1986 to 1991 he was employed at NeXT Computer, Inc., responsible for sound, music, and signal processing software for the NeXT computer workstation. After NeXT, he became an Associate Professor at the Center for Computer Research in Music and Acoustics (CCRMA) at Stanford, teaching courses and pursuing research related to signal processing techniques applied to music and audio systems. Continuing this work, he is presently a Professor of Music and Associate Professor of Electrical Engineering (by courtesy) at Stanford University. For more information, see http://ccrma.stanford.edu/~jos/.