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1,o,-----------,----------" Y Ol------+----------j NORMALIZED 1.0 SPECTRUM 0.8 -1.0"-----------L------ 71 . 0 0,2 -I~ 0 -Lf\ {\ [7 V \ f----l~--+_-+--4 ~'-------------- (B) X ~f\f\f\( IlJ\JlTV (0) (Fl ~~ 0.6 0.4 0O~I2~4:--:6---::-8--r-;::10---------... HARMONIC (AI (e) (EI IJ\ AAAAIt/I ~Vl/VVVv U_ (G I Fig. 13-31. Example nonlinear transfer function. (A) First-order Chebyshev polynomial, Y = X. (8) Second-order Chebyshev polynomial, Y = 2X2 - 1. (C) Third-order Chebyshev polynomial, Y = 4X 3 - 3X. (D) Fourth-order Chebyshev polynomial, Y = aX 4 - aX 2 + 1. (E) Fifth-order Chebyshev polynomial, Y = 16X s - 20X3 + 5X. (F) Sixth-order Chebyshev polynomial, Y = 32X 6 - 4aX 4 + laX 2 1. (G) Seventh-order Chebyshev polynomial, Y = 64X 7 - 112X s
476 MUSICAL ApPLICATIONS OF MICROPROCESSORS (H) l A AAu r rVl/\J\T V lL~ (Il (J I Fig. 13-31. (cont.) + 56X 3 - 7X. (H) Eighth-order Chebyshev polynomial, Y 128XB - 256X 6 + 160X4 - 32X2 + 1. (I) Combination of fourthand seventh-order Chebyshev polynomials, Y = 0.5 [T 4 (X) + T 7 (X)]. (J) Combination of first eight Chebyshev polynomials, Y = 0.28 [T,(X) + 0.72T2(X) + 0.36T 3 (X) + 0.57T 4 (X) + 0.42T 5 (X) + 0.25T 6 (X) + 0.16T 7 (X) + 0.12T B (X)]. (K) Contrived transfer function, Y = 0.42X + X3 exp (X - 1) sin (14 'ITX). N will produce only the Nth harmonic of the input sine wave. Note that when the curve describes an odd function (the shape to the left ofthe Y axis is the negative image of the shape to the right) only odd harmonics are created. Likewise, when it is an even function (the shape to the left is a positive image of the shape to the right), only even harmonics are created. Figure 13-311 and J shows that two or more Chebychev polynomials can be added together to get a controlled mixture of harmonics in direct proportion to the amount of each polynomial included. Note that, in this case, the resulting polynomial must be scaled to restrain the output waveform amplitude to unity. In Fig. 13-31K, an arbitrary mixture of polynomial, exponential, and trignometric functions is used to create the curve. Its spectrum has harmonics out to the 30th and a desirable gently rolling spectral envelope. Thus, it is apparent that nonlinear waveshaping can produce any arbitrary amplitude spectrum just as direct waveform table scanning could. In fact, one could consider the process as simply scanning a waveform table with a sine wave rather than a sawtooth wave as in the direct procedure. The preceding analysis only holds when the input sine wave is of unit amplitude. If the amplitude is reduced, the spectrum will change. Generally, the upper harmonics will decline more rapidly than the lower ones as the
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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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60 MUSICAL ApPLICATrONS OF MICROPRO
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82 MUSICAL ApPUCATIONS OF MICROPROC
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84 MUSICAL ApPUCATIONS OF MICROPROC
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vvv·(B) 86 MUSICAL ApPLICATIONS OF
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100 MUSICAL ApPLICAnONS OF MICROPRO
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Table 5-1. 6502 Instruction Set Lis
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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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Page 438 and 439: DIGITAL TONE GENERATION TECHNIQUES
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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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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 777 f
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21 Future Frequently, when glvmg ta
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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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Musical Applications of Microproces
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