## 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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Definition of a Signal

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Alternative Realizations