
70 CHAPTER 4. IIR DIGITAL FILTERS
4.3.2 IIR Filter Notation
IIR filters are more complicated than FIR filters, and there are various choices the designer
must make when implementing them. The remainder of this chapter will focus primarily
on implementation issues associated with IIR filters. Recall that the generalized difference
equation associated with a causal IIR filter is
M
k=0
a[k]y[n − k]=
N
k=0
b[k]x[n − k]
or in output variable form,
a[0]y[n]=−
M
k=1
a[k]y[n − k]+
N
k=0
b[k]x[n − k].
The a[0] term, the coefficient of y[n], is usually normalized to 1. In fact, MATLAB nor-
malizes the a[0] coefficient prior to almost all of its calculations. This normalization ...