Digital Signal Processing Reference
In-Depth Information
elliptic are also matched very closely and can be judged equivalent except for the
discontinuities in the stopband caused by the zeros for the elliptic case.
A filter designer's task is not always clear cut. It seems that every project
requires as much stopband attenuation as possible while providing a phase
response as linear as possible. The task becomes one of weighing the importance
of each characteristic. If phase response is more critical than magnitude response,
then the Butterworth filter is a better choice. If the opposite is true, the elliptic
filter is a better choice. If magnitude and phase responses are nearly equal in
importance, then one of the Chebyshev filters may be the best choice. Other
alternatives are also possible. Elliptic filters can be used for their selectivity, with
phase compensation filters added to make the phase more linear. (These filter
types are not covered in this text, but references in the analog filter design section
of Appendix A provide further information.) A designer must be careful when
pursuing these alternatives, since in some cases the result may be no better than
the equivalent Butterworth or Chebyshev filter.
2.7 CONCLUSION
In this chapter, we studied the core of analog filter design, the normalized
approximation functions. By developing these functions, we have laid the
foundation for the remainder of the chapters on analog filter design as well as a
good bit of digital IIR filter design. By approaching each approximation function
in the same manner, and developing methods for determining exact pole and zero
placement, we have simplified the job of generating the C code necessary to
implement these algorithms in a clean, efficient manner. (Those who are interested
in seeing more on the development of the C code can turn to Appendix D.) In the
next chapter, we will finish up the analog filter design calculations by determining
a technique to unnormalize the transfer functions we have just developed.
