At this point, we can make following remarks:
1. The IIR filter output yðnÞ depends not only on the current input xðnÞ and past inputs xðn 1Þ, .,
but also on the past output(s) yðn 1Þ, ., (recursive terms). Its transfer function is a ratio of the
numerator polynomial over the denominator polynomial, and its impulse response has an infinite
number of terms.
2. Since the transfer function has the denominator polynomial, the pole(s) of a designed IIR filter
must be inside the unit circle on the z-plane to ensure its stability.
3. Compared with the finite impulse response (FIR) filter (see Chapter 7), the IIR filter offers a much
smaller filter size. Hence, the filter operation requires a fewer number of computations, but the
linear phase is not easily obtained. The IIR filter is preferred when a small filter size is called
for but the application does not require a linear phase.