of Microprocessors

DIGITAL FILTERING 487
where 0 is now the output of the filter. Although this is certainly slower in
BASIC because of the extra statement, it is likely to be much faster in
assembly language because of the elimination of a multiplication operation.
At this point one can repeat the Fig. 14-2 experiment with several
different frequencies to observe the typical R-C low-pass characteristic,
which was done to create Fig. 14-3. Note that near the O.SF} point the
-6 dB/octave cutoff slope decreases somewhat. This is due to actual aliasing
of the filter response, since it is not zero at or beyond Fs/2. As digital filters
are studied, it will be found that their amplitude response always tends to
depart from the ideal as the Nyquist frequency is approached.
One can also apply digital square waves to the filter and observe that
the output samples show the same kind of leading edge rounding that the
analog filter exhibits. In fact, the samples of the square-wave response (step
response in general) are exactly the same as ADC samples from the response of
an analog R-C low-pass filter would be. A digital filter having this property
is said to be impulse invariant, which for our purposes means that the time
domain response is the same as the corresponding analog filter.
Signal Flow Graphs
Although the calculations involved in a digital filter can be represented
as equations or program fragments, they do not give a very clear picture of the
AMPLIFIER WITH GAIN OF 0314
MULTIPLIES INPUT SAMPLES BY 0314
MIXER OR ADDER
ADO SAMPLES A AND B TOGETHER AND SuBTRACT C TO PRODUCE
THE OUTPUT SAMPLE
-[J-
ONE SAMPLE PERIOl) DELAY
SAVE THE INPUT SAMPLE FOR ONE SAMPLE PERIOD AND THEN PASS
ON TO THE OUTPUT
Fig. 14-4. Symbols used in signal flow graphs