Summary and Conclusions

This concludes the discussion of time-domain filter descriptions, including difference equations, signal flow graphs, and impulse-response representations. More time-domain forms (alternative digital filter implementations) will be described in Chapter 9. A tour of elementary digital filter sections used often in audio applications is presented in Appendix B. Beyond that, some matrix-based representations are included in Appendix F, and the state-space formulation is discussed in Appendix G.

Time-domain forms are typically used to implement recursive filters in software or hardware, and they generalize readily to nonlinear and/or time-varying cases. For an understanding of the effects of an LTI filter on a sound, however, it is usually more appropriate to consider a frequency-domain picture, to which we now turn in the next chapter.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.