of Microprocessors

SOURCE-SIGNAL ANALYSIS 555
-5°
FH
FREQUENCY
(A)
°lrrt\\
-5 [
.~;::=
FREQUENCY
(8)
..
Fig. 16-7. Overlap between analyzer filters. (A) Insufficient overlap. (8) Excessive
overlap.
in Fig. 16-7A, there will be large frequency gaps that none of the filters
respond very strongly to. On the other hand, excessive overlap degrades
frequency resolution. Overlap can be characterized by noting at what attenuation
adjacent amplitude responses cross. A good number for the singlesection
bandpass used here is -6 dB or the 50% voltage response points. The
formula for Q based on a 6-dB bandwidth is: Q = 1. 732Fc/(Fh-FI).
Table 16-1 and Fig. 16-8 show the 30-channel bandpass responses
with overlap at the 6-dB points. What is plotted in Fig. 16-8 is the gain
versus frequency for each filter after it has been normalized for unity gain at
the center frequency. This would seem to be the only reasonable way to
normalize filter gains, but a peculiar thing happens if one feeds white noise
into the analyzer. Some channels, notably the high-frequency wide
bandwidth ones, report a higher amplitude than others even though the
input sound has a flat spectrum!
The uneven response is due to the fact that white noise has constant
power per hertz of bandwidth, and the wider bandwidth filters therefore
absorb more power. A typical complex music spectrum would show the
same results. On the other hand, a sound having only a few widely spaced
harmonics would be analyzed correctly! The only way to avoid this dilemma
is to use equal bandwidths for all of the filters. If wider bandwidths are
desired at the higher frequencies, two or more bands can be averaged, which
does not create problems. Even though the spectral data are reduced, computation
time soars. The filterbank analyzer, therefore, is best suited for rough
analysis of dense (lots of frequency components) spectra, in which case the
channel gains are normalized for equal response to white noise.
The low-pass filters following the rectifiers must also be specified. As
was mentioned earlier, their primary job is to smooth ripple from the rectifier
without unduly slowing response to sudden spectrum changes. However,
one must be careful to avoid multisection sharp cutoff filters because
their step response includes a lot of ringing, which would distort the
analysis. A reasonable compromise is a resonant low-pass with a Q of around
0.8. Since the spectrum sample rate is 100 Hz, a cutofffrequency of30 Hz or
so is indicated. Acceptable ripple rejection in the lowest band may require a