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.
Definition of a Signal