of Microprocessors

DIGITAL FILTERING 499
the turnover frequency (at a constant "Q" value), the delay of the cascade is
inversely proportional to frequency.
The audible effect of fixed all-pass filters is generally subtle, but
dynamic variation of the filter parameters can have a dramatic effect. Consider,
for example, a cascade of four all-pass filters each with the same
turnover frequency and a relatively broad transition width. Next, assume a
I-kHz sine wave tone fed through the filters. If the filter turnover frequencies
are high, such as 10 kHz, the tone will be phase shifted very little. If the
turnover frequency is allowed to rapidly decrease, the tone will experience a
constantly increasing phase shift up to a maximum of 1,440° or four cycles
when the turnover frequency has decreased to 100 Hz or so.
During the turnover frequency transition, however, the tone coming
out of the filter had a lower instantaneous frequency! Reversing the sweep
will produce a momentary higher frequency. The speed of the transition
determines the peak frequency deviation. If the signal entering the filter has
numerous harmonics, the temporary frequency shift will "ripple" audibly
through the harmonics as the turnover frequency shifts. By driving the
turnover frequency parameter with a low-frequency periodic or random signal,
a chorus-like effect can be obtained.
OUTPUT
OUTPUT
~tvvv~
o O.5/T 1.5/T 2.5/T
FREQUENCY
(A)
~:VVyy
liT 2/T 3/T
FREQUENCY
( B)
Fig. 14-13. Cosine (A) and sine (8) comb filters
Digital Notch Filters
Although a standard notch filter response can be created by suitable
setting of the cannonical digital filter constants, other more interesting and
useful variations are possible. The comb filter mentioned in Chapter 2 is one
ofthese that is very simple to produce in a digital synthesis system. The filter
is consttucted by splitting the signal into two paths, inserting a time delay in
one of the paths, and mixing the signals together in equal proportions as
shown in Fig. 14-13. The filtering effect is produced by phase cancellation
between the delayed and undelayed signals. At very low frequencies, the
delay line in Fig. 14-13A has essentially no effect on the phase of the signal
so it reinforces the undelayed signal in the mixer. When the frequency