IIR filter design - Continuous and Discrete Time Signals and Systems - page 741

there are a large number of applications where an appropriate filter (FIR or IIR)
is chosen based on implementation cost and robustness.

16.5.3 Delay

The propagation delay between the time an input signal is applied and the time
when the output appears is another important factor in filter selection. Because
of the larger number of implementation elements, the FIR filters generally have
a larger delay than the IIR filters.

16.6 Summary

This chapter presented transformation techniques, namely the impulse invari-
ance and bilinear transformations, used to design IIR filters. These transforma-
tion techniques are based on converting the frequency specifications H ( Ω )of
IIR filters from the DT frequency Ω domain into the CT frequency specifica-
tions H ( ω ). Based on the CT frequency specifications, a CT filter with transfer
function H ( s ) is designed, which is then transformed back into the original DT
frequency Ω domain to obtain the transfer function H ( z ) of the required IIR
filter. Section 16.2 introduced the impulse invariance transformation used to
design lowpass filters. The impulse invariance method uses a linear expression,

= ω T ,

Ω

where T is the sampling interval, to convert DT specifications to the CT domain.
Because of the sampling process, the impulse invariance method suffers from
aliasing when transforming the analog filter H ( s ) to the digital filter H ( z ). A
consequence of aliasing is that the order N of the designed filter H ( z ) is much
higher than the optimal design. To prevent aliasing, Section 16.3 presented
the bilinear transformation, which transforms the DT specifications to the CT
frequency domain using the following expression:

− 1 ( ω/ k ) .

ω = k tan( Ω / 2) or Ω = 2 tan

The transfer function H ( s ) of the CT filter is then transformed into the z-domain
using the following transformation:

= 1
k

z − 1
z + 1 ,

s

in which k is generally set to unity. Section 16.4 extended the design techniques
to highpass, bandpass, and bandstop filters.
A comparison of IIR and FIR filters was presented in Section 16.5. We
demonstrated that the order of the FIR filter is generally higher than that for IIR