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DIGITAL-TO-ANALOG AND ANALOG-TO-DIGITAL CONVERSION 371 Sign-Magnitude Coding Looking again at the curves in Fig. 12-2, it is seen that the maximum SiN ratio of 96 dB for a 16-bit DAC occurs right at the point of overload. In a real listening situation, this would correspond to the peak of the loudest crescendo in the piece. At the ear-shattering volume this might represent, one is highly unlikely to notice a noise level scarcely louder than a heartbeat. On the other hand, duting extremely quiet passages when the noise would be noticed most, the noise level remains unchanged meaning that the SiN ratio has degraded. It would be nice ifsome of the excess SiN at high signal levels could be traded off for a cheaper DAC without affecting or even improving the SiN at lower signal levels. This, in fact, is possible and can be accomplished in at least three different ways. Although not specifically mentioned previously, an audio DAC must be connected so that both positive and negative voltages can be produced. Normally, this is accomplished by offset binary coding and shifting the normally unipolar DAC output down by exactly one-half of full scale. In audio applications, a de blocking capacitor is sufficient for the level shifting. Low signal levels imply that the net DAC output hovers around zero. An offset binary DAC, however, sees this as one-half scale. In Chapter 7, it was determined that the most significant bit of the DAC had the greatest accuracy requirement; therefore, it is logical to assume that the greatest linearity error would occur when the MSB switches. Unfortunately, this occurs at half scale also so this kind of DAC imperfection would directly subtract from the SiN ratio at low signal levels as well as high. Thus, with offset binary coding, one must use a highly linear DAC. The sign-magnitude method of obtaining a bipolar DAC output does not suffer from this problem. Using the basic circuit configuration that was shown in Fig. 7-17, small signal levels will only exercise the lesser significant DAC bits, thus eliminating the noise caused by errors in the most significant bits. As a side effect, the sign-bit amplifier provides the equivalent of one additional bit of resolution making a 16-bit DAC act like a 17-bitter! The significance of all this is that inexpensive DACs with 16 bits of resolution but only 13 or so bits of linearity are available. When linearity is less than resolution it means that the most significant bits are off enough to make the DAC nonlinear at the points where the affected bits change. A 16-bit DAC with 13-bit linearity could have nearly an eight-step gap or backtrack right at 1/2 scale, lesser errors at 1/4 and 3/4 scale, and an even smaller error at 1/8, 3/8, 5/8, and 718 scale. If connected in an offset binary circuit, it would perform no better than a 13-bit DAC. But when connected in a sign-magnitude circuit, we have just the tradeoff that we have been looking for as the curve in Fig. 12-3 shows.
372 MUSICAL ApPLICATIONS OF MICROPROCESSORS 100 90 80 70 i5 60 >= Q: g UJ 50 ~'" °6 + z 40 ...J Z * 30 20 10 -~~0!-:0:-----='90:---""8:'::0---:!70:---""6:'::0----}5~0---4:'::0'------~30'::---'f.:
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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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82 MUSICAL ApPUCATIONS OF MICROPROC
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vvv·(B) 86 MUSICAL ApPLICATIONS OF
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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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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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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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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 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 771 +
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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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