Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 390

Table 8.13 Comparisons of Three IIR Design Methods
Design Method

BLT Impulse Invariant Pole-Zero Placement

Filter type Lowpass, highpass,

bandpass, bandstop

Appropriate for lowpass
and bandpass

Second-order for
bandpass and band
stop; first-order for
lowpass and highpass

Linear phase No No No

Ripple and stopband
specifications

Used for determining
the filter order

Used for determining
the filter order

Not required;
3 dB on passband
offered

Special requirement None Very high sampling

relative to the cutoff
frequency (LPF) or to
upper cutoff frequency
(BPF)

Narrow band for BPF or
notch filter;
lower cutoff frequency
or higher cutoff
frequency for LPF or
HPF.

Algorithm complexity High: Frequency

prewarping,
analog filter design,
BLT

Moderate: Analog filter
design
determining digital
impulse response;
apply z-transform

Low: Design
equations

Minimum design tool Calculator, algebra Calculator, algebra Calculator

BLT ¼ blinear transformation; LPF ¼ lowpass filter; BPF ¼ bandpass filter; HPF ¼ highpass filter.

comparison. The performance of the impulse-invariant method is satisfactory in the passband.
However, it has significant performance degradation in the stopband when compared with the other
two methods. This is due to aliasing when sampling the analog impulse response in time domain.
Improvement in using the pole-zero placement and impulse-invariant methods can be achieved by
using a very high sampling rate. Example 8.30 describes the possible selection of the design method by
a DSP engineer to solve a real-world problem.

EXAMPLE 8.30
Determine an appropriate IIR filter design method for each of the following DSP applications. As described in
a previous section, we apply a notch filter to remove the 60-Hz interference and cascade a bandpass filter to
remove noise in an ECG signal for heart rate detection. The following specifications are required:
Notch filter:
Harmonics to be removed ¼ 60 Hz
3dB bandwidth for the notch filter ¼ 4Hz
Bandpass filter:
Passband frequency range ¼ 0.25 to 40 Hz
Passband ripple ¼ 0.5 dB
Sampling rate ¼ 600 Hz