of Microprocessors

460 MUSICAL ApPLICATIONS OF MICROPROCESSORS
B
fifth harmonic by 0.12 X 2n before each record IS calculated and thus
generate the correct average frequency.
Unfortunately, there is a substantial glitch where the records are
spliced together as shown in Fig. 13-21B. This is due to the fact that the
wave frequency within the records is still 195 Hz and the entire phase
correction takes place between the 'records. Such discontinuities are quite
objectionable. If there was a way to spread the correction throughout the
record, perhaps the results would be better.
One method of accomplishing spreading involves the concepts of record
overlap and interpolation. Overlap means that the end of one record overlaps
the beginning of the next rather than butting up against it. Time-variable
interpolation is used to combine the overlapping portions of the records into
a single string of samples in the overlap area. With this technique, the sharp
discontinuities seen earlier are spread out over the overlap interval.
Figure 13-22 shows some possibilities for overlapping and interpolation.
Figure 13-22A shows an overlap factor of 50%, which means that 50%
of the time there is overlap between records. Thus, a new record is started
every 0.75 times the record length. figure 13-22B shows 100% overlap
where a new record is started when the previous one is only half complete.
Even higher orders of overlap are possible. Obviously, overlapping results in
more computation, since more records are needed per unit time.
The interpolation needed in the overlap areas is accomplished with the
same method described earlier regarding interpolation between two
waveform tables. One requirement is that the "weighting curves" always
sum up to 1. 0 during the overlap interval. A linear curve is the simplest that
RECORD
DURATION
~
I N I
I N+I
1------1
RECORD
PERIOD = 0.75
RECORD DURATION
OVERLAP
INTERVAL
t-1
t N+2 N+4 I
OVERLAP INTERVAL
I~I
N I N+2 N+4 N+6
N+3 N-II N+J N+3
I_I
RECORD
PERIOD= 0.5
RECORD DURATION
(A) (8)
N+5
1.0~, .r-~/--,/
o
~~
RECORD RECORD
N • N+I
(ci
1.0 o /"......../ -~.-~ ......../'
'-v-~
RECORD RECORD
N N+ I
(D)
1.0
0.5
o
'-v-~
RECORD RECORD
N N+I
(E)
Fig. 13-22. Record overlap and interpolation. (A) 50% overlap. (8) 100% overlap.
(C) Interpolation curves for 50% overlap. (0) Linear interpolation
for 100% overlap. (E) sin 2 interpolation for 100% overlap.