9.1 CHAPTER OBJECTIVES
On completion of this chapter, the reader should be able to
1. design a Butterworth or Chebyshev prototype analog low-pass filter and plot its response;
2. scale an analog low-pass filter to a given cutoff and transform it to a high-pass or bandpass characteristic;
3. take an analog filter design and create a digital filter approximation; and
4. understand the possible shortcomings of the conversion from an analog to digital filter design and compensate for those where possible.
This chapter covers recursive filters, that is, filters with “memory.” This is another class of filter; in some ways, recursive filters are complementary to the nonrecursive filters discussed previously, and they may be an appropriate alternative in many situations. Recursive filters are generally more difficult to design but often result in lower-order filters as compared to nonrecursive filters. This means that they require less memory and fewer computational resources to implement, as well as having an output after a shorter time period. However, the trade-off is a more involved design process. This chapter considers the design of recursive filters using the classical method of analog filter prototyping. Although a brief introduction to continuous systems is given, some prior exposure to continuous systems theory is desirable.
9.2.1 Defining a Recursive Filter
With the exception of the notch filters introduced in Chapter 8, all of ...