of Microprocessors

490 MUSICAL ApPLICATIONS OF MICROPROCESSORS
desirable properties. First, it was a second-order filter with independent control
of center frequency and Q. Next, a single circuit simultaneously provides
low-pass, bandpass, high-pass, and notch outputs from a single input. Finally,
it could be tuned over a very wide range of both frequency and Q
merely by varying just three resistors (two for frequency and one for Q) or
alternatively, three gain factors. Precise matching of the two frequencydetermining
controls was not necessary unless a deep notch was desired.
Since all second-order response functions are available from this one circuit,
it is an ideal building block for sharper and more complex filters.
Figure 14-6 shows the analog state-variable filter in terms ofamplifiers
and integrators. Taking this and the diagram of a digital integrator, the
digital state-variable filter follows almost trivially. (Note that the configuration
of the first integrator has been altered somewhat. It is necessary to have a
delay inside the overall feedback loop for the network to function.) All of the
desirable characteristics of the state variable have been retained. The four
different outputs are still present and frequency and Q are independently
adjustable. A count of arithmetic operations reveals that five additions (six if
the notch output is needed) and three multiplications per sample are required.
Although more efficient structures are possible for single-function
filters such as bandpass, they are not nearly as flexible and give up independence
between center frequency and Q control.
Using the rules just discussed, let us convert this diagram into a series
of BASIC statements. Before starting, the names of variables must be established.
For convenience with the limited names allowed in BASIC, the
following will be arbitrarily assigned:
I Input sample
L Low-pass output sample
B Bandpass output sample
H High-pass output sample
N Notch output sample
F 1 Frequency control parameter
Q 1 Q control parameter
D1 Delay associated with bandpass output
D2 Delay associated with low-pass output
The first task is to compute all of the outputs. The sequence of computation
is important in order to minimize the statements and to avoid having a
variable depend on itself in the same time period. Careful examination of the
diagram reveals that if the low-pass output is evaluated first, everything else
falls into place. Thus, the first step is accomplished by the following
statements:
1000 LET L=D2+Fl*D1
1001 LET H=I-L-Q1*D1
1002 LET B=F1*H+D1
1003 LET N=H+L