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DIGITAL FILTERING 495 OUTPUT Fig. 14-9. Cannonical second order digital filter amplitude response curve, while the feedforward paths cause response dips or zeroes. Note that the same design equations for the filters given earlier can be applied to the cannonical form with any unused constants set to zero. Because of its generality, this structure is ideal for use in a genetal-purpose filtering subroutine or hardware implementation as a digital filter module. All-Pass Digital Filter One important type of filter that has not yet been discussed is the all-pass filter. As its name implies, it is not a frequency-discriminating filter and in fact passes all frequencies equally well with unity gain. Instead, its purpose is frequency-sensitive phase shift. All filters shift phase in varying amounts as a natural consequence of frequency discrimination, but the allpass filter exhibits phase shift alone. Consequently, an all-pass network can be used to correct for the phase shift of a regular filter without disturbing its amplitude response. In synthesis applications, however, it is used to introduce a time-varying, frequency-sensitive phase shift to otherwise stationary sounds, thereby imparting added richness to the sound. Before looking at the filter itself, the relation between phase shift and time delay should be understood. Either parameter can be plotted as a function of frequency as in Fig. 14-10. One type of all-pass filter is a simple delay line. As shown in Fig. 14-lOA, an ideal delay line has constant delay independent of frequency. Its phase shift, however, is a linear function of frequency as shown in Fig. 14-lOB. This can be explained by noting that at very low frequencies the 500-1LSec delay is only a small fraction ofa cycle. At 500 Hz, which is a 2,000-J.Lsec period, the 500-J.Lsec delay becomes a quarter cycle phase lag or -90°. At 1 kHz, the delay becomes a half cycle and so on. At higher frequencies, the phase-shift magnitude continues to increase, but it is customary to plot the principal value of the shift. Thus, the curve shifts up to 180° leading and continues its decline from there. In mathematical terms, the delay curve is the derivative (proportional to slope) of the phase curve or, conversely, the phase curve is the integral
496 MUSICAL ApPLICATIONS OF MICROPROCESSORS E!o-----,--1,o~O'""'0--...,2,...,,0!-:'0c:"0--c:"3,-fcio:-:0:-----:4'"",O':-OO=---- FREOUENCY (Hz) (A) 270 CJ 7~ ~ ...J ị ., 1Il « :I: 0.. 180 90 '"« ...J -180 -270 FREQUENCY (Hz) (B) n~_~ o 100 200 300 400 500 600 700 BOO 900 FREQUENCY (Hz) O~-':;:I:::::i:!:::::::J.==""""'.... (C) 1k IB0- j 0 ~ 90 ~ -90 « :I: 0.. -/80 FREQUENCY (0) (Hzl Fig. 14-10. Phase and delay graphs. (A) Delay versus frequency of 500-fl-sec delay line. (8) Phase versus frequency of 500-fl-sec delay line. (C) Delay of a highly dispersive filter. (D) Phase of a highly dispersive filter. (proportional to area under a curve) of the delay curve. As a result, only one curve is needed to fully characterize the delay/phase behavior of the filter. For musical purposes, the most useful all-pass filters exhibit nonlinear phase shifts and therefore time delays that vary with frequency. This means that a sharp transient, which contains a wide range of frequency components, will exit from the filter with the frequency components separated and
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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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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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300 MUSICAl ApPLICATIONS OF MICROPR
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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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Page 460 and 461: DIGITAL TONE GENERATION TECHNIQUES
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Page 496 and 497: DIGITAL FILTERING 483 Input Samples
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Page 541 and 542: 528 MUSICAL ApPLICATIONS OF MICROPR
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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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