of Microprocessors

DIGITAL-TO-ANALOG AND ANALOG-TO-DIGITAL CONVERSION 393
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TIME (msecl
Fig. 12-21. Step response of five-section Q.25·dB Chebyshev filter (1
cutoff)
kHz
the worse its phase shift will be right before cutoff (the phase after cutoff is
not important, since the signal is greatly attenuated). Poor phase response in
a filter also means poor transient response, which is evident in Fig. 12-21,
which shows the response of the five-section 0.25-dB Chebyshev to the
leading edge of a square wave.
The ringing waveform is due to the four peaked low-pass sections that
make up the filter. Since they are sharper, elliptical filters are even worse,
while Butterworth types, although much better, are still far from perfect. It
is important to realize, however, that, while this might be characterized as
poor transient response for a filter, it is quite good compared to normal audio
standards, particularly for speakers. The majority of the ringing is right at
the top edge of the passband, and, while it appears to imply a large peak in
the response, we have seen that it only amounts to 0.25 dB. Also note that
such an isolated step function should never come from the DAC, since it
implies the synthesis of frequencies far beyond one-half the sample rate.
Thus, this filter characteristic should not be confused with what hi-fi
critics term poor transient response, which is usually a mid- and lowfrequency
phenomenon. In any case, a decision must be made between a
sophisticated filter and low sample rate or a simpler filter with better transient
response and a higher sample rate.
Finite Sample Width Compensation
Earlier it was mentioned that if the DAC output was actual steps or
pulses of finite width a slight high-frequency rolloff was inevitable. Figure