SOFTWARE VS. HARDWARE
`A RECONCILIATION
`
`SYNTHESIS;
`
`2244 (B-9)
`
`Dana
`
`C. Massie
`
`E-Mu
`Santa
`
`Systems,
`Cruz,
`
`Inc.
`California
`
`Evan
`
`Brooks
`
`and
`
`Peter
`
`Gotcher
`
`Digidesign,
`Palo
`Alto,
`
`Inc.
`California
`
`Presented at
`the 78th Convention
`1985May 3-6
`Anaheim
`
`AUDI0
`
`®
`
`Thispreprint has been reproduced from the author's advance
`manuscript, without ed/ting, corrections or consideration by
`the Review Board. The AES takes no respons/b//ityfor the
`contents.
`
`Additional preprints may be obtained by sending request
`and remittance to the Audio Engineering Society, 60 East
`42nd Street, New York, New York 10165 USA.
`
`,4//rights reserved. Reproduction of thispreprint, or any
`portion thereof, is not permitted without direct permission
`from the Journal of the Audio EngineeringSociety.
`
`AN AUDIO ENGINEERING SOCIETY PREPRINT
`
`Vestas Ex 1034-p. 1
`Vestas v GE
`
`
`A RECONCILIATION
`
`SYNTHESIS;
`
`2244 (B-9)
`
`Dana
`
`C. Massie
`
`E-Mu
`Santa
`
`Systems,
`Cruz,
`
`Inc.
`California
`
`Evan
`
`Brooks
`
`and
`
`Peter
`
`Gotcher
`
`Digidesign,
`Palo
`Alto,
`
`Inc.
`California
`
`Presented at
`the 78th Convention
`1985May 3-6
`Anaheim
`
`AUDI0
`
`®
`
`Thispreprint has been reproduced from the author's advance
`manuscript, without ed/ting, corrections or consideration by
`the Review Board. The AES takes no respons/b//ityfor the
`contents.
`
`Additional preprints may be obtained by sending request
`and remittance to the Audio Engineering Society, 60 East
`42nd Street, New York, New York 10165 USA.
`
`,4//rights reserved. Reproduction of thispreprint, or any
`portion thereof, is not permitted without direct permission
`from the Journal of the Audio EngineeringSociety.
`
`AN AUDIO ENGINEERING SOCIETY PREPRINT
`
`Vestas Ex 1034-p. 1
`Vestas v GE
`
`
`
`Softwarevs. HardwareSynthesis;A Reconciliation
`
`Dana C. Massie
`E-Mu Systems,
`Inc.
`SantaCruz,CA
`
`EvanBrooks
`Peter Gotcher
`Digidesign,Inc.
`PaloAlto, CA
`
`computer music system is described
`An integrated
`which combines
`an Emulator
`II polyphonic
`digital
`sampling keyboard and a Macintosh personal
`computerto permit
`flexible analysis,modification,
`and synthesis
`of musical signals. System
`capabilities include algorithms such as weighted
`overlap-add
`phase
`vocoder,
`non-linear
`waveshaping,time-varyingadditivesynthesis,
`Karplus Strong, graphical editing of synthesis
`parameters and waveforms, and efficientreal-time
`performance of sounds.
`
`Introduction
`
`A brief survey of the history of computer music reveals the
`great division between the flexibility
`of non real-time
`software music synthesis and the efficiency of real-time
`hardware synthesis. The Emulator II and Macintosh/Sound
`Designersystem is anideal compromisebetween software and
`hardwarestrategies for music synthesisandperformance.The
`Emulator II is a real-time performance instrument providing
`large amounts of sound memory for audio storage, and the
`Sound Designer program provides non real-time (but fast)
`display, analysis,modification, andsynthesisof audiosignals.
`
`Macintosh is a trademark licensed to Apple Computers, Inc.Emulator Il is a
`trademark nf F-Mu Sv_tPrn_. Inr
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`I. History
`
`Very early in the development of computers several
`prominent researchers recognized the potential musical
`applications of computers. At Bell Laboratories, computer
`programs (Music V, BLODI) for signal synthesis, analysis,
`display, andmodification were in usein the early 1960's[1,2,3].
`Although software signal processing algorithms running on
`used [4,5],
`genera] purpose computers are still
`these
`techniquesare virtually unknownoutside of the research and
`academiccommunities.
`
`Any digital signal processing or synthesis algorithm can be
`implemented in software,
`typically much easier than in
`hardware. Also, design
`changes
`can typically
`be implemented
`much faster in software than in hardware. Manyof today's
`digital
`processors and synthesizers were originally
`implemented
`in software,
`including
`the digital
`reveri)erator
`and the FM synthesizer
`[6,7].
`
`The price of software synthesis flexibility is non real-time
`computation.
`A general
`purpose
`computer,
`well-suited
`for
`rapid developmentof new processingtechniques,is not nearly
`fast enoughto perform anybut the simplest of computationsin
`real-time.
`Instead,
`processing
`and
`performance
`are two
`separate steps, with performance occuring in real-time but
`with processingtaking as muchas 100times longer (somtimes
`more,
`for very complex
`algorithms).
`An analogy would be to
`play apianoandto haveto wait overnight to hearits sound.
`
`Cumbersomesyntax is the second major drawback of most
`existing computer musiclanguages.Anarcaneuser interface is
`required for even the simplest of musical scores,
`thus
`alienating all but the most dedicated of composers. If all
`pianists had to learn FORTRAN(or its equivalent) in order to
`play the piano, chances are that we might never hear
`Beethovenagain...
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`The tremendousflexibilityof softwaresynthesishas not
`overcomethe disadvantagesof its nonreal-time computation.
`As a result, almost without exception, sound synthesis,
`analysis, and processing are now performed by real-time
`hardware.Suchhardware typically is restricted to a single
`algorithm. A hardwareFMsynthesizer cangenerate FMsounds
`but.cannot,provide the filter sweeps of old fashioned analog
`synthesizers.
`
`I1.The Emulator and the Macintosh Hardware
`
`The Emulator II is a polyphonic digital sampling keyboard.
`Internally, it
`is a muitiprocessor computer specialized for
`music.Optimized for real-time performanceand studio work,
`it. canrecord anysoundandplay it back immediately from the
`keyboard, transposablein pitch by up to five octaves.A block
`diagramof one Emulatorchannelis shownin figure 1.Memory
`for storage of up to seventeensecondsof audiocanbe divided
`into as many as gg separate recordings. A high-speed
`microprogrammed bipolar microcontroller
`arbitrates
`asynchronousmemory accessrequestsfromtheeightoutput
`channeldigitaltoanalogconvert,ors.A variablesamplingrate
`isusedto transposepitchratherthana variablesampling
`increment(skippingorrepeatingsamples),whichcanproduce
`aliasing or imaging distortion. Eachoutput channelhasits own
`independant 4-pole voltage-controlled lowpass filter
`(VCF)
`andvoltage-controlled amplifier (VCA),both with independant
`four-phase ADSR envelope generators and low frequency
`oscillators.
`
`The real-time data structures used in the Emulator permit
`considerable live performance control and expressive
`capability. The 61-note keyboard is velocity sensitive, with
`velocity
`assignable to seven major parameters; VCA
`amplitude, VCA attack time, VCF cutoff
`frequency, VCF O
`(resonance), Velocity Crossfade and Velocity Switch. The
`Velocity Crossfadefeature crossfadesbetween two differen[
`voices as a function of key velocity, while the velocity switch
`selects oneof two voices basedonkey velocity.
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`Sustain of short sounds is accomplished by "looping", or
`repeating a specified section of the waveform.Most sampling
`instrumentsprovide this feature in someform. TheEmulatorII
`provides two different types of looping, forwardsandforwards
`backwardslooping. Whena sound is in the backwards mode,
`these loop types are reversed. An auto-loop algorithm is
`provided to optimize the initial user supplied loop points. The
`loop points are movedto achievethe best match betweenthe
`loop end and the loop start. The searchis performed over a
`50- millisecond region (one period at 20 Hertz). Auto-looping
`makes finding loop points a faiMy painless process, usually
`removinganyspliceglitchesonthefirstiteration.
`
`Apple Computer'sMacintoshcomputer provides an excellent
`environment
`for
`interactive
`software music synthesis
`programs. Its 68000 microprocessor provides efficient 32-bit
`arithmetic, essential
`for computationally intensive signal
`processing algorithms. The high resolution bit-mapped
`graphics display is a necessity for presenting the voluminous
`data produced by signalanalysisprograms.TheMacintoshalso
`providesextensiveoperatingsystemsupportforwindowing,
`graphics,andmouse-baseduserinterfacefeatures.An 8-bit
`D-A convertorandspeakerisavailab)eforsoundoutput.
`
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`III. SoundDesigner Functions
`
`A. Sound Data Transfer
`
`Digitized sounddata interchange between the Emulatorand the
`Macintoshis accomplishedby a500-kilobaud RS-422serial data
`link, with block
`parity
`and retransmission
`of
`faulty
`blocks. Such
`a high speed link
`is crucial
`to the overall
`efficiency
`of
`the
`Sound Designer environment.Soundsdigitized by the Emulator
`can be rapidly transferred to the Macintosh for display and
`modification; soundssynthesized or stored in the Macintoshcan
`be rapidly
`transferred back to the Emulator
`for
`live
`performance. A two-second sound file (typical of a good
`instrument sample for Emulator use) can be transferred in a
`little over a second.
`
`B. Waveforrn Display with Cut and Paste Editing
`Paradigms
`
`Up to three separate sound waveforms can be displayed
`simultaneously. Horizontal and vertical zoom is provided to
`allow display of the entire soundwaveforrn or magnificationof
`minute details. Using the mouse to select waveform regions,
`sections of a soundcanbe removed (cut) or copied andinserted
`(pasted) into any other waveforTnregion. Reminiscent of the
`tape splicing of music concrete, delicate "microsurgery" canbe
`performed on sound events without
`the tedium of
`tape
`manipulation.Figures 2 thru 4 showa recording of a handclap at
`three different scale factors. The early reflections from a
`reverberator are readily apparent.
`
`C. Time-Frequency Spectrum Analysis
`
`Spectrum analysis with three-dimensional
`time frequency
`display provides
`important analytical capabilities. Currently
`implemented is a radix-two decimation in time FFT,with a
`Hammingwindow.Animportant distinction shouldbe madehere;
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`this is a time frequency analysis. The FFT is performed
`repeatedly on successivesections of the waveform showingthe
`variation of spectrum with time. A number of computer music
`instruments perform static spectrum analysis for a single
`waveform segment.Static spectrum analysis is of little value
`for typical musicalsignalswith non-stationary spectra.
`
`intermediate results and block floating point
`Thirty-two bit
`arithmetic are used to maximize dynamic range without
`sacrificing computational efficiency. A 256 point complex FFT
`takes less than 150 milliseconds to complete. With the 68000,
`an important technique canbe easily usedto reduce the error
`from roundingintermediate results of the FFTcomputation.A
`traditional method for multiplication of two complex numbers
`ZI andZ2 on afixed-point machineis as follows.
`With Z1= XI + JYIandZI: X2 +JY2,the computedproduct is
`
`[Z1Z2]= [X1X2]r-[Y1Y2]r+ J([Y1X2]r+[XIY2]r)
`
`where []r refers to the process of roundinga 32-bit result to
`!6-bits whichinjects errors (noise) into the signal.
`
`Thefollowing techniquereducesthis error by afactor of two.
`
`[ZIZ2] '- [X1X2- YI Y2]r +J[YIX2+ X1Y2]r
`
`Essentially, this process involves keeping full 32-bit accuracy
`until the complex multiply is complete, rather than truncating to
`16-bit valuesfor the intermediate results [8]. Implementingthis
`with the 32-bit
`registers of
`the 68000 proved to be
`straightforward.
`
`Currently under developmentare anumberof extensions to the
`FFTanalysis features now running,the most ambitious of which
`Jscertainly the weighted overlap-add phasevocoder [9,10].This
`
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`
`
`is a general short-time analysis/resynthesis _chemeused for
`some years at various university and industry research sites.
`Usingthe phasevocoder provides the capability to perform a
`numberof highly Unusualmodifications. Inaddition to traditional
`cross-spectralsynthesiscommon to traditionalanalog
`vocoders(i.e.,talkingflutes),signalscanbe transposedinpitch
`independentlyofdurationortimescaledindependentlyofpitch,
`bothwithveryfew artifacts(i.e.glitchingcharacteristicofold
`harmonizeralgorithms).As wellasallowingpitchtransposition,
`signalspectracanberescmledtominimizetheformantshifting
`("munchkin")effectoftraditionalpitchtransposition.Frequency
`domainnoisereductionisanotherimportantapplicationofthe
`phasevocoder[11,12,13].
`
`E. Direct Digital Synthesis
`
`For many years, researchers at various universities have been
`inventing newsynthesis algorithms for direct digital synthe?.is
`of music,most of whichhavenever left the academicworld. With
`the Emulator II as the output device, synthesized soundsneed
`only be 2 to ;5secondslongto be useful.With suchashort sound,
`a fast computer (the Hacintosh) can compute the result of a
`synthesis program in only a few seconds.A whole composition
`need not be generated as in traditional computer music, only
`individual soundswhichcanthen be played back in real-time on
`the Emulator.
`
`Software synthesis algorithms currently planned or already
`implementedfor Sound Designer include
`
`1.Karplus-StrongPluckedString Algorithm.
`2. FMSynthesis with multiple carriers [14,15]. The Yamaha
`DX7hasmadethis techniquevery popular.
`3.Non-LinearWaveshaping[ 16,17]
`4. Simple WaveformGeneration(sine, band-limited square,
`sawtooth)
`5. Piece-wise Log-Linear SegmentEnvelopeGenerators.All
`of the synthesis algorithms will share a commongraphical
`envelope generator entry technique.
`
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`
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`6.Time-Varying Additive Synthesis.
`7. Variable Filtering techniquesincludingIowpass,highpass,
`resonant,and multiple bandfiltering with envelope generator
`inputs.
`
`a matter
`is simply
`algorithms
`Adding additional
`software, not manufacturingnewhardware.
`
`of writing
`
`new
`
`Ratherthan describe these synthesis techniquesin detail (all
`of them have been well described in the literature), we will
`describe the Karplus-Strong algorithm to illustrate Sound
`Designer's features.
`
`rich
`computer music algorithm to yield
`the simplest
`Possibly
`timbres, the PluckedString algorithm invented by Karplusand
`Strong
`of Stanford University
`is very efficient
`[18]. First a RAM
`buffer X[n] is filled with P samplesof randomdata where P is
`the desired period length. Successive periods are derived
`from the first
`by a recursive
`averaging
`procedure;
`
`for K = 0 to Numberof Periods in RAMBuffer
`for n = 0 to P
`
`XK[n] = (XK _lin] + XK_lin-1] ) / 2
`
`of 90 is
`length
`period
`from an original
`The waveform resulting
`scale factor
`in figure 6
`shown in figures
`5 and 6. The horizontal
`in the wave form. The
`is greatly magnified
`to show details
`decay time
`for
`the Nth harmonic
`falls off approximately
`as
`p3/N2 whichcanbe seenin the time-frequency spectra] plot in
`figure
`7. Control
`of
`this most basic form of
`the Plucked String
`algorithm
`consists
`simply
`of
`setting
`the
`original
`pitch.
`Extensionsto the algorithm suchas decay stretching andusing
`other soundfiles instead of randomdata as the initial buffer
`will be implemented.
`
`F. Time Domain Signal Processing
`
`A series of
`
`important
`
`time domain signal processing
`
`-8-
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`
`
`and
`
`attack
`
`algorithms will be available. Includedare:
`I. Amplitude scaling of asignal.
`2. Amplitude normalization (scaling of signal amplitude to
`maximum gain)
`3. Merge/Mix of
`two signals using a user specified
`constant-power
`crossfade
`function.
`4. Sample Rate Conversion
`to allow optimum sample rate to
`conserve RAM,or to changethe pitch (and duration) of the
`signal data. Sound tuning can be adjusted
`on playback
`from the
`Emulator II, but. if
`two sounds are to be digitally combined
`which are slightly out, of
`tune, sample rate conversion is
`necessary.
`5. Dynamic Range Compression with variable
`release
`time constants.
`and both
`resonant.,
`highpass,
`6. Equalization
`with lowpass,
`example
`is
`equalizer
`high and low shelving
`[19,20]. A shelving
`is a simple
`illustrated
`in figures
`8 thru
`10. This equalizer
`the filter
`second order equalizer. The computations for
`coefficients
`were
`derived
`from a
`conformal mapping
`procedure
`taken
`from [19]. The use of block
`floating
`point.
`prevents numerical overflow from the recursive filter, while
`sacrificing
`little
`computational
`efficiency.
`The block
`size
`typically
`is 256 samples.
`The original
`signal
`in figure
`8 is a
`tom-tom drum. The time domain waveforTns are shown before
`and aft. er having been equalized with ! 8 dB boost, at
`I kHz. The
`signal
`is normalized
`after
`equalization
`(to prevent
`saturation),
`so the output waveform (t.op waveform)
`shows a much lower
`apparent,
`amplit.ude,
`even though the peak amplitude
`is the
`same. The spectral
`plot
`is shown in figure 9 before EO., and in
`figure
`10 after
`EO Notice
`f.he dramatic
`difference
`in high
`frequency
`content.. This example
`shows a possible
`use of
`the
`waveshaping
`algorit.hm To reduce the peak to average power
`ratios,
`t.he non-linear
`waveshaping
`algorithm
`could
`be used t.o
`generate soft clipping of the equalized waveform. This soft.
`to the dipping almost, always
`clipping would be similar
`encounteredin recording soundswith a high peak-t.o-average
`ratio, suchas drums.
`
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`
`
`G.Emulator Parameter Editing
`
`Graphicalediting of performanceparameters of the Emulator II
`will also be implemented.Theparameters that make the most
`sense to control using a graphical mouse-driven environment
`
`1.Envelopes
`VCA envelopesand Filterenvelopeswillbe shown
`graphicallyon the same display.The relationshipbetween
`filter and VCA envelopes is important since a fast VCA
`envelopecanrender irrelevant a slowfilter envelope.
`2.KeyboardVoice Assignment
`can
`The placement
`of up to 99 voices on the keyboard
`benefit greatly from visual assistance. Icons for individual
`voices will be usedto showthe rangesof voice placement.
`3. Looping
`and Truncation
`The placement of loop points and the truncation of
`soundstart andend points canbe helpedby graphicaldisplays.
`
`Conclusions
`
`Wehope that the approachof using ajudicious combinationof
`non real-time
`processing
`with a real-time
`sampling
`instrument
`will provide muchnew raw material for musicalcomposition in
`anefficient andeconomicalenvironment.
`
`Acknowledgements
`We would like to thank the people at the Computer Audio
`ResearchLaboratory at the Centerfor MusicExperimentat the
`University of California, San Diego, especially Andy Voelkel,
`Mark Dolson,D.Gareth Loy, and F.RichardMoore for all their
`patient assistance.We also wish to thank the people at the
`Center for Computer Research in Music and Acoustics at
`Stanford University,
`particulary
`Rob Poor, Bernard
`Mont-Reynaud,andJulius O.Smith. Finally, many thanks go to
`DavidRossum,Scott Wedgeand MarcoAlpert of E-MuSystems
`
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`for'[heir encouragementandassistance.
`References
`
`1.Mathews,Maxet al. "TheTechnologyof ComputerMusic",MIT
`Press,Boston 1969
`
`2. Risset, Jean-Claudeand Max Ma[hews,"Analysis of Musical
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`1969
`
`3.Kelly,J. L.,C.LochbaumandV.A.Vyssotsky, "A BlockDiagram
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`4. Moore,F.Richard"TheComputerAudio ResearchLaboratory
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`5 Kowalski, MichaelJ. and Andrew Glassner"The NYITDigital
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`6. Schroeder,M.P,"ColorlessArtificial Reverberation,J Audio
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`14. Schottstaedt, Bill, "The Simulation of Natural Instrument
`Tones using FrequencyModulationwith a ComplexModulating
`Wave,"ComputerMusicJournal, Volume 1,Number4:46-50
`
`15.LeBrun,Marc,"A Derivation of the Spectrum of FMwith a
`ComplexModulatingWave,"ComputerMusicJournal, Volume I,
`Number 4:51-52
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`Synthesis,"
`"Digital Waveshaping
`16. LeBrun, Marc,
`EngineeringSoc.,Volume27, pp250-265,April ! g7g
`
`J. Audio
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`17. Arfib, D., "Digital Synthesis
`Multiplication of Nonlinear Distorted Sine Waves," J. Audio
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`
`of
`Digital Synthesis
`lg83"
`18. Karplus, K. and A. Strong
`Plucked-String
`and Drum Timbres."
`Computer Music Journal,
`Volume 7 Number 2:43-55
`
`James A., "The Manifold Joys of Confonmal Mapping:
`I g. Moorer,
`to Digital
`Filtering
`in the Studio,"
`J. Audio
`Applications
`Engineering Soc., Volume 31, pp826-840,
`November
`Ig83
`
`-12-
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`
`
`Micro-Control
`
`l er
`
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`
`_
`
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`
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`
`OutDut
`
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`
`..i;:"i
`
`........
`
`fill
`
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`Convertor
`
`)elope Gen.
`
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`iiii
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`Il!,.!.!.!.!,..,,!.I..L!.,l..!....!.!.,L!..!.!.J.!.!J..l
`
`Figure
`block
`
`II voice
`Emulator
`1. A single
`diagram
`form.
`The wavetable
`
`in
`shown
`is
`shared
`
`between
`
`the eight
`
`output
`
`channels.
`
`Vestas Ex 1034-p. 14
`Vestas v GE
`
`
`
`20. Smith, Julius O. and James B. Angell, "A Constant-Gain
`DigitalResonator Tuned by a Single Coefficient,"Computer
`MusicJournal,Volume6,Number4:36-40
`
`-13-
`
`Vestas Ex 1034-p. 15
`Vestas v GE
`
`
`
`ds File Edit Display L'alibrate Tools Mode Extras
`
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`r,
`
`Figure 2. This display
`sound-
`shows an entire
`file of hand-claps. Here the early
`reflections
`are easily
`of a reverberator
`seen, as well as
`the sound. The vertical
`the overall
`envelope
`of
`scale shows a little
`over 200 milliseconds
`per
`window.
`
`k --
`
`id
`
`Vestas Ex 1034-p. 16
`Vestas v GE
`
`
`
`File Edit Display Calibrate
`_E]_miWi_
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`Tools Mode Extras
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`
`shown
`3. The same hand-claps
`,Figure
`1. More
`the magnification
`of
`figure
`visible
`of
`the individual
`hand-claps.
`along the upper
`The Icons
`left
`are for
`various
`signal
`functions,
`synthesis,
`selection,
`play
`sound,
`selection,
`cursor
`selection,
`etc.
`k
`
`at
`detail
`
`twice
`is
`
`the display
`of
`including
`wave
`calibration
`
`Vestas Ex 1034-p. 17
`Vestas v GE
`
`
`
`Display
`
`Calibrate
`
`Tools Mode
`Untitled"
`
`EHtras
`
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`File
`
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`
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`
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`2
`
`msec
`_ Scale
`
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`
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`
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`
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`
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`po
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`
`the hand-claps.
`of
`even more detail
`Magnification
`can be to lhe single
`
`factor-of-two
`Figure 4. A furtherlevel.
`
`sample
`zoom shows
`
`]
`
`Vestas Ex 1034-p. 18
`Vestas v GE
`
`
`
`File Edit Display Calibrate
`
`Tools Mode Extras
`
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`
`
`
`
`
`waveform
`5. Synthesized
`Figure
`plucked
`by the Karplus-Strong
`shows
`algorithm.
`This display
`milliseconds
`of
`the attack
`of
`
`produced
`string
`the first
`the sound.
`
`25
`
`\
`J
`
`1
`
`Vestas Ex 1034-p. 19
`Vestas v GE
`
`
`
`I_ File Edit Display Calibrate Tools Mode Extras
`
`
`-^ .........':j_.,1--¥L5-.............
`u."ii;-,-
`
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`
`two periods
`
`over
`Figure 6. A little
`waveform from figure
`cursor
`is placed at 26.08 milliseconds
`(the cursor
`coordinates
`are shown at
`lower
`!eft.).
`
`of
`
`5 are shown here. Thel
`
`the
`
`1
`
`the
`
`Vestas Ex 1034-p. 20
`Vestas v GE
`
`
`
`I_ File Edit Display Calibrate lools Mode Extras
`
`--
`
`_
`
`......
`
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`
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`
`
`
`
`
`
`the sound
`of
`Figure 7. A spectrum analysis
`shown in figures
`5 and O. The horizontal
`axis
`is increasing
`frequency
`to the right, with
`time represented
`in the z-axis,
`and energy
`in the vertical
`axis. Notice
`how the high
`frequencies
`decay faster
`than low frequencies
`The fundamental
`is almost
`constant
`amplitude.
`This is a 256 point
`sliding
`analysis.
`
`FFT
`
`Vestas Ex 1034-p. 21
`Vestas v GE
`
`
`
`r
`
`_
`
`File Edit
`
`Illindows
`
`Display
`
`Calibrate
`
`Tools Mode Debug
`
`/_
`
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`
`-=-Ui
`
`_
`
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`
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`Q
`
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`Illaveform
`Display
`
`is shown
`drum recording
`8. A tom-tom
`Figure
`a
`with
`processing
`here before
`and after
`The
`digital
`shelving
`high-pass
`equalizer.
`waveform
`in the lower
`display
`is pre-eq.,
`the upper
`display
`is after
`18 dB boost
`at
`1 kHz. The peak amplitude
`is the same in both
`cases, even though
`the amplitude
`appears
`less
`in the upper waveform.
`
`and
`
`Vestas Ex 1034-p. 22
`Vestas v GE
`
`
`
`-__
`
`lllaueformOi_ptay___5_
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`
`the tom-tom
`of
`Figure 9. A spectrum analysis
`drum before equalization.
`Low frequency
`components
`are almost all
`that are visible
`in this
`display.
`
`Vestas Ex 1034-p. 23
`Vestas v GE
`
`
`
`_:
`
`IllavufDrm
`
`Ol_pluy
`
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`
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`
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`1,0
`
`
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`
`
`
`Figure I O. A spectrum analysis
`equalization.
`The high frequency
`(18 d6 e !kHz)
`is easily
`visible.
`
`after
`boost
`
`Vestas Ex 1034-p. 24
`Vestas v GE
`
`
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