Page 249 - Analog and Digital Filter Design

246 Analog and Digital Filter Design

as the filter order increases, the peak in the group delay approaches the pass-
band cutoff frequency.

The effect of a nonconstant group delay on impulsive signals is to produce
increased ripple, particularly near the pulse edges. This is sometimes described
as “ringing” because it looks like a decaying resonance. Distortion can be so
severe as to cause misdetection in the pulse-detecting electronics. This effect is
shown in Figure 9.2, where the output response of a sixth-order 1.2kHz lowpass
Butterworth filter is given when a 200 Hz square wave is applied at its input.

x:= 1,2.. 1000 A:=1

L
0 500 1000
X
Figure 9.2
Group Delay and Band-Limited Response

In Figure 9.2 the third harmonic is being delayed by 0.2 radians (about 11.5”)
and the fifth harmonic is being delayed by 1.5 radians (about 86”). Had the fifth
harmonic experienced a delay of 0.4 radians the delay would have been pro-
portion to frequency. The resultant waveform would have been a delayed version
of that given in Figure 9.1.

The Solution: All-Pass Networks
All-pass filters are so named because they have a flat frequency response; all
signals are passed without attenuation. They are also sometimes known by their