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DIRECT COMPUTER SYNTHESIS METHODS 107 1.0 0.8 0.6 0.4 0.2 o 0 50 100 150 200 / -0.2 -0.4 -0.6 -0.8 -1.0 TIME (}I5.c) (AI 1.0 0.8 0.6 0.4 ii'O }l5tC I 0.2 oi=.If:!.l.J..!±!fJ-!,!:!:li~~~L.LLLlllll.WJ..U.IL.LLLL..rrTTT1TrrrTTTTTTTTTT1TmrTTTTTTTTTT1Trr~9;;:50;,;;1.0::e;OO 50 100 150 200 250 -0.2 -0.4 -0.6 -0.8 -1.0 ~ w 0 g -25 f- ::; -50 ll. '" -75 , '" -100 L....I ,AI,-----'c-~-...J/II ,-----,::'-:-----:::!:-:--... V 99 101 V 199 201 FREQUENCY (kHz) (C) Fig. 4-1. (A) 1-kHz sine wave divided into 100 10iLSec portions. (B) Sine wave approximation from DAC. (C) Spectrum of B. pulses spaced at lO-fLsec intervals. Each individual pulse or the number it represents is called a sample because it gives the waveform amplitude at a sample point in time. The frequency of the pulses is called the sample rate and in this case it is 100 ks/s (kilosamples per second). The sample rate is almost
108 MUSICAL ApPLICATIONS OF MICROPROCESSORS always constant, although it is conceivable that changing it to match the current degree of change in the waveform might be desirable. As was demonstrated earlier, waveform appearances can be deceiving when human hearing perception is involved so the spectrum of Fig. 4-IB is shown in Fig. 4-1C. The interesting point about the spectrum is what is not present. One would think that distortion components would be spread throughout the spectrum at perhaps reduced amplitude compared with the desired I-kHz component, but such is not the case for the lOO-dB range shown. The first visible extraneous component is very strong but occurs at 99 kHz, well beyond the rang\; of hearing and audio recording devices. Thus, the conclusion is that sampling of the I-kHz sine wave at a 100-kHz rate is more than adequate for its high-fidelity reproduction. Proof ofFidelity Some skepticism is expected at this point, so an attempt at an informal proof will be made. Consider a string of narrow pulses of constant height as in Fig. 4-2A. This is an exactly repeating waveform so its spectrum consists of harmonics of 100 kHz. Note that at least for the harmonics shown they are all of equal amplitude. Since the pulse widths must be finite, however, a point is reached at which higher frequency harmonic amplitudes decrease. As an aside, note also that a train of narrow pulses is the only waveform whose spectrum is the same shape as the waveform itself. If this pulse waveform is one input of a balanced modulator and an accurate, pure I-kHz sine wave is the other input, the output would be exactly the waveform shown previously in Fig. 4-IB. Recall from Chapter 2 that a balanced modulator is really a multiplier that produces an output that is the instantaneous product of the two inputs. Examination of the two input waveforms and the output shows this to be true. It should also be recalled 1.0 0.66 0.33 -0.33 -0.66 -1.0 Of----'-----'---'--L-I-..I-+-!-'-----'--'--'--I--'--'-.L-JL_-..l--'-__ TIME (,usec) (A) o -20 -40 -60 -80 O~.I~.2--'--L-I--'-.L-L-I--"~MHc:cz-'---L-I-..l-'--L-I--'-~2-'-:M- FREQUENCY (MHz) (B) Fig. 4-2. Properties of a string of pulses. (A) String of narrow pulses. (B) Spectrum of A.
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Musical Applications of Microproces
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© 19B5 by Hayden Books A Division
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serve to acquaint the general reade
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SECfrON II. Computer-Controlled Ana
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17. Digital Hardware 589 AnalogModu
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1 Music Synthesis Principles Creati
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MUSIC SYNTHESIS PRINCIPLES 5 own ar
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MusIC SYNTHESIS PRINCIPLES 7 Increa
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MUSIC SYNTHESIS PRINGPLES 9 VERY SM
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MUSIC SYNTHESIS PRINOPLES 11 repres
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MUSIC SYNTHESIS PRINCIPLES 13 The w
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MUSIC SYNTHESIS PRlNCIPLES 15 was c
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MUSIC SYNTHESIS PRlNOPlES 17 In act
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MUSIC SYNTHESIS PRINCIPLES 19 SIN (
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MUSIC SYNTHESIS PRINCIPLES 21 lILt!
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MUSIC SYNTHESIS PRINCIPLES 23 - ,--
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MUSIC SYNTHESIS PRINOPLES 25 + or--
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MUSIC SYNTHESIS PRINCIPLES 27 Human
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MUSIC SYNTHESIS PRINOPLES 29 fundam
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MUSIC SYNTHESIS PRINCIPLES 31 frequ
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MUSIC SYNTHESIS PRINCIPLES 33 from
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MUSIC SYNTHESIS PRINCIPLES 35 ever,
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MUSIC SYNTHESIS PRINCIPLES 37 have
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MUSIC SYNTHESIS PRINCIPLES 39 No li
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MUSIC SYNTHESIS PRINCIPLES 41 cropr
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44 MUSICAL ApPLICATIONS OF MICROPRO
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Table 5-1. 6502 Instruction Set Lis
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160 MUSICAL ApPLICATIONS OF MICROPR
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Coding Table 5-3. 68000 Addressing
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Table 5-4. 68000 Instruction Set Su
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Table 5-4. 68000 Instruction Set Su
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6 BasicAnalogModules Probably the m
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BASIC ANALOG MODULES 179 tage remai
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BASIC ANALOG MODULES 181 Op-amps ma
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BASIC ANALOG MODULES 183 '0: :? u
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BASIC ANALOG MODULES 185 with an id
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BASIC ANALOG MODULES 187 EXPONENTIA
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BASIC ANALOG MODULES 189 (or 0.9766
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BASIC ANALOG MODULES 191 4R Vr'o'M
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BASIC ANALOG MODULES 193 tooth with
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BASIC ANALOG MODULES 195 +IOVrel PU
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BASIC ANALOG MODULES 197 Table 6-1.
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BASIC ANALOG MODULES 199 constants
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BASIC ANALOG MODULES 201 12 ~ E 1-
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BASIC ANALOG MODULES 203 R2 R3 100
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BASIC ANALOG MODULES 205 fore, must
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BASIC ANALOG MODULES 207 For peak p
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BASIC ANALOG MODULES 209 22 pF RI S
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BASIC ANALOG MODULES 211 INPUT~OUTP
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BASIC ANALOG MODULES 213 Voltage-Tu
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BASIC ANALOG MODULES 215 +20 +15 +1
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BASIC ANALOG MODULES 217 100 ko. BA
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BASIC ANALOG MODULES 219 +15 V0----
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Digital-to-Analog and tlnalog-to-Di
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DIGITAL-TO-ANALOG AND ANALOG-TO-DIG
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11 CORtrolSequeRce Display andEditi
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CONTROL SEQUENCE DISPLAY AND EDITIN
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SECTIONIII DigitalSynthesis antl So
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Table 12·1. Design Data for Chebys
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~ o Table 12·1. (Cont.) Ripple = 1
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13 Digital Tone Generation Teehniqu
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DIGITAL TONE GENERATION TECHNIQUES
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Sample Number Harm. No. o 2 3 4 5 6
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Sample Spectrum Number 0 1 2 3 4 5
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1,0 0,8 0,6 0.4 0,2 °0 10 12 14 16
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1,o,-----------,----------" Y Ol---
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14 DigitalFiltering In analog synth
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DIGITAL FILTERING 483 Input Samples
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DIGITAL FILTERING 485 the input wav
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DIGITAL FILTERING 487 where 0 is no
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DIGITAL FILTERING 489 BAND REJECT >
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DIGITAL FILTERING 491 Next the inpu
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DIGITAL. FILTERING 493 circuits mak
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DIGITAL FILTERING 495 OUTPUT Fig. 1
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DIGITAL FILTERING 497 INPUT ~8~~~~~
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DIGITAL FILTERING 499 the turnover
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DIGITAL FILTERING 501 frequency is
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+ 3 1 oL-_-...l__---l__---L__---r-_
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DIGITAL FILTERING 505 When programm
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DIGITAL FILTERING 507 lowest freque
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DIGITAL FILTERING 509 Even with a p
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DIGITAL FILTERING 511 OUTPUT Fig. 1
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DIGITAL FILTERING 513 INPUT VARIABL
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DIGITAL FILTERING 515 INPUT (C) -(.
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DIGITAL FILTERING 517 NOTE: Xl, Y,
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DIGITAL FILTERING 519 AMPLITUDE, (d
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DIGITAL FILTERING 521 o ~ -10 ~ -20
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DIGITAL FILTERING 523 1.0 0.8 0.6
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DIGITAL FILTERING 525 When the outp
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16 Source-SignalAnalys,is One of th
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SOURCE-SIGNAL ANALYSIS 545 nOdB T I
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--------, I I ! II i I I I I , , i"
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SOURCE-SIGNAL ANALYSIS 549 3 IN -"
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SOURCE-SIGNAL ANALYSIS 551 Data Rep
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SOURCE-SIGNAL ANALYSIS 553 SIGNAL B
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SOURCE-SIGNAL ANALYSIS 555 -5° FH
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SOURCE-SIGNAL ANALYSIS 557 -5 -10 ~
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SOURCE-SIGNAL ANALYSIS 559 Since th
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SOURCE-SIGNAL ANALYSIS 561 o -5 -10
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SOURCE-SIGNAL ANALYSIS 563 o -5 -10
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SOURCE-SIGNAL ANALYSIS 565 overlapp
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SOURCE-SIGNAL ANALYSIS 567 • ....
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SOURCE-SIGNAL ANALYSIS 569 from an
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SOURCE-SIGNAL ANALYSIS 571 componen
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SOURCE-SIGNAL ANALYSIS 573 and some
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SOURCE-SIGNAL ANALYSIS 575 185491 A
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SOURCE-SIGNAL ANALYSIS 577 SYSTEM F
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SOURCE-SIGNAL ANALYSIS 579 (AI (BI
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SOURCE-SIGNAL ANALYSIS 581 (Gl II'
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SOURCE-SIGNAL ANALYSIS 583 PULSE PE
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SOURCE-SIGNAL ANALYSIS 585 again, t
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SOURCE-SIGNAL ANALYSIS 587 Quite ob
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17 DigitalHardware At this point, w
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DIGITAL HARDWARE 591 Lsa I N+I DIVI
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DIGITAL HARDWARE 593 (~OCK[ L _ LSB
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DIGITAL HARDWARE 595 FREQUENCY CONT
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DIGITAL HARDWARE 597 Fig. 17-7. Pha
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DIGITAL HARDWARE 599 MOST SIGNIFICA
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DIGITAL HARDWARE 601 waveform chang
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DIGITAL HARDWARE 603 As an example,
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DIGITAL HARDWARE 605 1. Sixteen ind
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DIGITAL HARDWARE 607 discussed, the
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DIGITAL HARDWARE 609 between the 41
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DIGITAL HARDWARE 611 8-BIT PORT I M
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FREOUENCY CONTROL IN I I 20 FREOUEN
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DIGITAL HARDWARE 615 TO MULTIPLEXED
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FREQ. :a.-8 CNTL. WRITE FREQ. I 20
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DIGITAL HARDWARE 619 effective freq
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DIGITAL HARDWARE 621 The signal mem
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DIGITAL HARDWARE 623 into a filter
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DIGITAL HARDWARE 625 made using con
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DIGITAL HARDWARE 627 A Hybrid Voice
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DIGITAL HARDWARE 629 o -5 -10 -15 ~
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DIGITAL HARDWARE 631 o -5 -10 -15 ~
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DIGITAL HARDWARE 633 D3 02 01 10 00
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DIGITAL HARDWARE 635 plementers on
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DIGITAL HARDWARE 637 taken care of
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SECTIONIV ProductApplications andth
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716 MUSICAL ApPLICATIONS OF MJCROPR
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RING MOD VCD A PITCHo--+lcNTL OUT A
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20 Low-CostSYllthesis Techniques Wh
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LOW-COST SYNTHESIS TECHNIQUES 759 g
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LOW-COST SYNTHESIS TECHNIQUES 761 i
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LOW-COST SYNTHESIS TECHNIQUES 763 0
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LOW-COST SYNTHESIS TECHNIQUES 765 S
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LOW-COST SYNTHESIS TECHNIQUES 767 c
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LOW-COST SYNTHESIS TECHNIQUES 769 O
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LOW-COST SYNTHESIS TECHNIQUES 771 +
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LOW-COST SYNTHESIS TECHNIQUES 773 F
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LOW-COST SYNTHESIS TECHNIQUES 775 F
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LOW-COST SYNTHESIS TECHNIQUES 777 f
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21 Future Frequently, when glvmg ta
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LOW-COST SYNTHESIS TECHNIQUES 781 T
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LOW-COST SYNTHESIS TECHNIQUES 783 t
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LOW-COST SYNTHESIS TECHNIQUES 785 "
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LOW-COST SYNTHESIS TECHNIQUES 787 m
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LOW-COST SYNTHESIS TECHNIQUES 789 a
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Bibliography The following publicat
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BIBLIOGRAPHY 793 DMA DOS FET FFT FI
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(Communication) Minor - Computer Sc
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newsletter, writing numerous articl
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conversion subsystem, especially if
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In the beginning the company was su
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HAL : I really haven't kept up with
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was clear he was serious, I named m
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influences too like interrupts from
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SONIK : What activities do you do o
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as a homework assignment. So much o
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