of Microprocessors

432 MUSICAL ApPLICATIONS OF MICROPROCESSORS
1000 REM PROGRAM TO UTILIZE THE FOURIER SERIES TO FILL A WAVEFORM TABLE
1010 REM ARRAY A HOLDS THE AMPLITUDES OF THE HARMONICS
1020 REM ARRAY P HOLDS THE PHASES OF THE HARMONICS
1030 REM THE ZEROTH ELEMENT OF A AND P CORRESPONDS TO THE DC COMPONENT
1040 REM VARIABLE N HOLDS THE NUMBER OF THE HIGHEST HARMONIC TO PROCESS
1050 REM VARIABLE MHOLDS THE SIZE OF THE TABLE TO GENERATE
1060 REM VARIABLE Q IF 0 SELECTS RANDOM PHASES, IF 1 USES ARRAY P
1070 REM ARRAY T IS THE GENERATED TABLE WITH ALL ENTRIES BETWEEN BUT NOT
1080 REM INCLUDING -1 AND +1
1100 REM AMPLITUDE DATA
1110 DATA 0,.8,.6,.2,.55,1.0,.7,.3,.2,.1,.05
1120 REM PHASE DATA
1130 DATA 0,0, .2,.4,.7, .45, .1, .5, .85, .9,0
1140 LET N=10
1150 LET M=256
1160 LET Q=l
1200 REM SET UP THE AMPLITUDE AND PHASE ARRAYS
1210 FOR 1=0 TO N
1220 READ A( I)
1230 NEXT I
1240 FOR 1=0 TO N
1250 IF Q=O GOTO 1270
1260 READ P(I)
1270 GOTO 1280
1270 LET P(I)=RND(l)
1280 NEXT I
1300 REM MAIN LOOP TO COMPUTE PRELIMINARY TABLE CONTENTS
1310 FOR 1=0 TO M-1
1320 LET T(I )=0
1330 LET A1=6.28318*I/M
1340 FOR J=O TO N
1350 LET T(I)=T(I)+A(J)*COS(J*A1+6.28318*P(J))
1360 NEXT J
1370 NEXT I
1400 REM SCAN RESULTING TABLE FOR MAXIMUM ABSOLUTE VALUE
1410 LET A1=0
1420 FOR 1=0 TO M-1
1430 IF ABS(T(I)~A1 THEN LET A1=ABS(T(I))
1440 NEXT I
1500 REM NORMALIZE THE TABLE
1510 FOR 1=0 TO M-1
1520 LET T(I)=T(I)/A1*.99999
1530 NEXT I
1600 REM ADD CODE HERE TO OUTPUT THE TABLE IN SUITABLE FORM
1700 STOP
1800 END
Fig. 13-7. Program to optimally fill waveform tables
almost always produces waves with a single high-amplitude peak and low
average amplitude elsewhere, which is less than optimum for low noise. The
array T is the waveform table containing values between - 1 and + 1 when
the program returns. Additional code to convert the values into integers with
the appropriate range and to store them in the final waveform table is easily
added.
Assembly language can also be used to construct the table in 1% to
10% of the time required by a BASIC program. Part of the improvement is
due to more efficient program execution, while the rest is due to the use of