Summary

This chapter has provided an overview of practical digital filter implementation, analysis, transformation, and display. The principal time-domain views were the difference equation and the impulse response. The signal flow graph applies to either time- or frequency-domain signals. The frequency-domain analyses were derived from the z transform of the difference equation, yielding the transfer function, frequency response, amplitude response, phase response, pole-zero analysis, alternate realizations, and related topics. We will take up these topics and more in the following chapters.

In the next chapter, we begin a more systematic presentation of the main concepts of linear systems theory. After that, we will return to practical digital filter analysis, implementation, and (elementary) design.

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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.