Digital Signal Processing Reference
In-Depth Information
Chapter 7
Finite Impulse Response Digital Filter
Design
In the last chapter, we considered the design of digital filters based on the
approximation methods for analog filters. We investigated a number of ways that
the transfer functions in the analog domain could be converted to transfer
functions in the digital domain. In this chapter, we will develop methods that deal
with the digital filter as a unique filter type, not based on analog filter
approximation methods. The focus of this chapter will be on finite impulse
response (FIR) filters that have only a finite number of terms in their impulse
response. These filters have a number of advantages over the IIR filter types. An
FIR filter is always stable, realizable, and provides a linear phase response under
specific conditions. These characteristics make FIR filters attractive to many filter
designers. However, the major disadvantage of FIR filters is that the number of
coefficients needed to implement a specific filter is often much larger than for IIR
designs. A more complete comparison of IIR and FIR filters is given in Section
8.1.
We will begin this chapter with a standard method of designing FIR digital
filters using the Fourier series description of the desired frequency response. This
method will then be modified and improved by using a windowing technique to
improve the shape of the responses. In addition, the Parks-McClellan optimization
technique will be discussed as a technique of reducing the length of the resultant
FIR filters. Finally, the C code for determining the frequency response of FIR
filters will be developed.
7.1 USING FOURIER SERIES IN FILTER DESIGN
There are a number of methods that could be used to design FIR filters. We will
investigate one of the most popular in this section. Other methods are described in
the references listed in Appendix A for digital filter design.
161
