of Microprocessors

DIGITAL FILTERING 505
When programming according to the diagram, actually shifting the
data is very inefficient. Instead, a pointer to the current sample is maintained
and references to stored previous sample values are made relative to the
pointer. Figure 14-17 is a program in BASIC that implements the transversal
filter. The R array contains the impulse response, the S array contains
previous signal samples, and N is the number of impulse response samples.
The input sample is S 1 while the output sample is 52.
In order to make maximum use of the algorithm, it is helpful to know
some additional impulse response properties. First, if the filter has zero or
linear phase its impulse response will always be perfectly symmetrical. If
such a phase response is acceptable, the number of multiplications needed per
sample can be essentially cut in half by adding the symmetrical parts together
before multiplication as shown in Fig. 14-18.
There are limits to the technique too. Filters with low-frequency discrimination,
sharp cutoff slopes, or narrow peaks and dips in their amplitude
response tend to have long duration impulse responses and therefore will
require a lot of calculation. Thus, a simple bandpass or low-pass function is
better performed with one of the previous techniques. On the other hand, if
the amplitude response has a lot of peaks and dips, only the narrowest or
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SYMMETRICAL IMPULSE RESPONSE
Fig. 14-18. Simplification of Fig. 14-16 for symmetrical impulse response