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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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Transient Response, Steady State, and Decay