of Microprocessors

666 MUSICAL ApPLICATIONS OF MICROPROCESSORS
0353 210E 83
0354 2116 8A
0355 211E 96
0356 2126 A6
0357 212E B9
0358 2136 CF
0359 213E E7
0360 2146 00
0361 214E 19
0362 2156 31
0363 215E 47
0364 2166 5A
0365 216E 6A
0366 2176 76
0367 217E 7D
0368 2186
0369 2186
o ERRORS IN PASS 2
.BYTE $83,$83,$84,$85,$86,$87,$88,$89
.BYTE $8A,$8B,$8D,$8E,$8F,$91,$93,$94
.BYTE $96,$98,$9A,$9B,$9D,$9F,$A2,$A4
.8YTE $A6,$A8,$AA,$AD,$AF,$B2,$B4,$B7
.BYTE $B9,$BC,$BF,$Cl,$C4,$C7,$CA,$CD
.BYTE $CF,$D2,$D5,$D8,$DB,$DE,$El,$E4
.BYTE $E7,$EA,$EE,$Fl,$F4,$F7,$FA,$FD
.BYTE $00,$03,$06,$09,$OC,$OF,$12,$16
.BYTE $19,$IC,$IF,$22,$25,$28,$2B,$2E
.BYTE $31,$33,$36,$39,$3C,$3F,$41,$44
.BYTE $47,$49,$4C,$4E,$51,$53,$56,$58
.BYTE $5A,$5C,$5E,$61,$63,$65,$66,$68
.BYTE $6A,$6C,$6D,$6F,$71,$72,$73,$75
.BYTE $76,$77,$78,$79,$7A,$7B,$7C,$7D
.BYTE $7D,$7E,$7E,$7F,$7F,$7F,$7F,$7F
.END
Fig. 18--7. Waveform table filler (cant.).
sidered with smaller values giving faster computation. The scaling logic
assumes that NHARM is never greater than 16, although this can be extended
by modifying the scaling computation or restricting the amplitude
sum to less than 16.
Looking closer at FSEVAL, it is seen that the product of a harmonic
amplitude and a sine table entry is a full 16 bits. To avoid almost certain
overflow when other harmonics are added in, the product is shifted right four
times, which effectively moves the binary point between bits 11 and 10. This
increases the range to 16 and reduces the resolution to 1/2,048. The increased
range positively insures against overflow for up to 16 harmonics.
In scale, only the most significant byte of the 16-bit samples produced
by FSEVAL is examined. Peak determination is by comparing the absolure
value of the upper sample bytes with a current maximum, which is kept in
MAX. This maximum is incremented by one before returning. Note that the
binary point position of MAX is between bits 3 and 2.
The FILL routine normalizes the samples by simply dividing the 16-bit
sample returned by FSEVAL by MAX. Since the binary points are in equivalent
positions, the point position for the quotient will be between bits 6 and
7, making it a signed fraction ready for storage in the waveform table.
Incrementing MAX by one in SCALE is required to avoid overflow in the
division, which would occur when the peak point is divided by itself. U nfortunately,
this action also introduces an error that reduces the scaled
amplitude somewhat. Large values of MAX minimize this error, however.
Thus, when a harmonic spectrum is prepared, the strongest harmonic should
be given an amplitude of 0.996 (O.FF). A 16/32-bit arithmetic package
would reduce the error to insignificance but would be about three times
slower on the 6502. It is important to note that this error is only an
amplitude error; it does not introduce excess noise beyond that due to the
lower amplitude. Also note that only the highest peak is normalized. It is