Historical Overview of Audio Spectral Modeling
Julius Smith CCRMA, Stanford University
Music 421 Applications Lecture
January 7, 2014
Julius Smith Music 421 Applications Lecture – 1 / 50 Milestones in Audio Spectral Modeling
• Fourier’s theorem (1822) Outline • Telharmonium (1898) Telharmonium • Voder (1920s) Voder • Channel Vocoder Vocoder (1920s)
Phase Vocoder • Hammond Organ (1930s)
Additive Synthesis • Phase Vocoder (1966) FM Synthesis • Digital Organ (1968) Sinusoidal Modeling • Additive Synthesis (1969) Future • FM Brass Synthesis (1970) • Synclavier 8-bit FM/Additive synthesizer (1975) • FM singing voice (1978) • Sinusoidal Modeling (1985) • Sines + Noise (1988) • Sines + Noise + Transients (1988,1996,1998,2000) • Inverse FFT synthesis (1992) • Future Directions
Julius Smith Music 421 Applications Lecture – 2 / 50 Outline Telharmonium Voder Channel Vocoder Phase Vocoder Additive Synthesis FM Synthesis Sinusoidal Modeling Future Telharmonium (1898)
Julius Smith Music 421 Applications Lecture – 3 / 50 Telharmonium (Cahill 1898)
U.S. patent 580,035: “Art of and Apparatus for Generating and Distributing Music Electrically”
Julius Smith Music 421 Applications Lecture – 4 / 50 Telharmonium Rheotomes
Forerunner of the Hammond Organ Tone Wheels
Julius Smith Music 421 Applications Lecture – 5 / 50 Telharmonium Rotor: Forerunner of Hammond Organ Tone Wheels
Outline
Telharmonium • Telharmonium
Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis
FM Synthesis
Sinusoidal Modeling
Future
Julius Smith Music 421 Applications Lecture – 6 / 50 Outline Telharmonium Voder Channel Vocoder Phase Vocoder Additive Synthesis FM Synthesis Sinusoidal Modeling Future The Voder (1939)
Julius Smith Music 421 Applications Lecture – 7 / 50 The Voder (Homer Dudley — 1939 Worlds Fair)
[< http://davidszondy.com/future/robot/voder.htm
Julius Smith Music 421 Applications Lecture – 8 / 50 Voder Keyboard
http://www.acoustics.hut.fi/publications/files/theses/ lemmetty mst/chap2.html — (from Klatt 1987)
Julius Smith Music 421 Applications Lecture – 9 / 50 Voder Schematic
http://ptolemy.eecs.berkeley.edu/~eal/audio/voder.html
Julius Smith Music 421 Applications Lecture – 10 / 50 Voder Demos
• Video Outline • Audio Telharmonium
Voder • Voder Keyboard • Voder Schematic • Voder Demos
Channel Vocoder
Phase Vocoder
Additive Synthesis
FM Synthesis
Sinusoidal Modeling
Future
Julius Smith Music 421 Applications Lecture – 11 / 50 Outline Telharmonium Voder Channel Vocoder Phase Vocoder Additive Synthesis FM Synthesis Sinusoidal Modeling Future The Channel Vocoder (1928) (“Voice Coder”)
Julius Smith Music 421 Applications Lecture – 12 / 50 Vocoder Analysis & Resynthesis (Dudley 1928)
Analysis: Outline
Telharmonium • Ten analog bandpass filters between 250 and 3000 Hz: Voder Bandpass → rectifier → lowpass filter → amplitude envelope Channel Vocoder • Voiced/Unvoiced decision made • Vocoder Examples • Fundamental frequency F0 measured for voiced case Phase Vocoder
Additive Synthesis Synthesis:
FM Synthesis • Ten matching bandpass filters driven by a Sinusoidal Modeling
Future ◦ “buzz source” (voiced), or ◦ “hiss source” (unvoiced) • Bands were scaled by amplitude envelopes and summed • Said to have an “unpleasant electrical accent” Related Speech Models: • The Vocoder is an early source-filter model for speech • Linear Predictive Coding (LPC) of speech is another
Julius Smith Music 421 Applications Lecture – 13 / 50 Vocoder Filter Bank Analysis/Resynthesis
magnitude, or Outline magnitude and phase extraction Telharmonium
Voder A Channel Vocoder x0(t) xˆ0(t) • Vocoder Examples f
Phase Vocoder Data Compression, A Transmission, Additive Synthesis xˆ(t) x(t) x1(t) Storage, xˆ1(t) Manipulation, FM Synthesis f Noise reduction, ... Sinusoidal Modeling
Future
A xN−1 xˆN−1
f
Analysis Processing Synthesis
Julius Smith Music 421 Applications Lecture – 14 / 50 Channel Vocoder Sound Examples
Outline • Original Telharmonium
Voder • 10 channels, sine carriers Channel Vocoder • • Vocoder Examples 10 channels, narrowband-noise carriers
Phase Vocoder
Additive Synthesis • 26 channels, sine carriers FM Synthesis • 26 channels, narrowband-noise carriers Sinusoidal Modeling • 26 channels, narrowband-noise carriers, channels reversed Future • Phase Vocoder: Identity system in absence of modifications
• The FFT Phase Vocoder next transitioned to the Short-Time Fourier Transform (STFT) (Allen and Rabiner 1977)
Julius Smith Music 421 Applications Lecture – 15 / 50 Outline Telharmonium Voder Channel Vocoder Phase Vocoder Additive Synthesis FM Synthesis Sinusoidal Modeling Future The Phase Vocoder (1966)
Julius Smith Music 421 Applications Lecture – 16 / 50 Phase Vocoder Analysis for Additive Synthesis (1976)
Outline Analysis Model Synthesis Model ω ∆ω Telharmonium Channel Filter ak ak(t) k+ k(t) Voder Response A F ∆ω Sine Osc Channel Vocoder k
Phase Vocoder 0 ω ω k Out Additive Synthesis • Early “channel vocoder” implementations (hardware) only FM Synthesis
Sinusoidal Modeling measured amplitude ak(t) (Dudley 1939) • Future The “phase vocoder” (Flanagan and Golden 1966) added phase tracking in each channel • Portnoff (1976) developed the FFT phase vocoder, which replaced the heterodyne comb in computer-music additive-synthesis analysis (James A. Moorer) • Inverse FFT synthesis (Rodet and Depalle 1992) gave faster sinusoidal oscillator banks
Julius Smith Music 421 Applications Lecture – 17 / 50 Amplitude and Frequency Envelopes
ak(t) Outline
Telharmonium
Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis
FM Synthesis
Sinusoidal Modeling t ωk t φ˙k t Future ∆ ( )= ( )
0
t
Julius Smith Music 421 Applications Lecture – 18 / 50 Outline Telharmonium Voder Channel Vocoder Phase Vocoder Additive Synthesis FM Synthesis Sinusoidal Modeling Future Additive Synthesis (1969)
Julius Smith Music 421 Applications Lecture – 19 / 50 Classic Additive-Synthesis Analysis (Heterodyne Comb)
Outline
Telharmonium
Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis • Additive Analysis • Additive Synthesis
FM Synthesis
Sinusoidal Modeling
Future
John Grey 1975 — CCRMA Tech. Reports 1 & 2 (CCRMA “STANM” reports — available online)
Julius Smith Music 421 Applications Lecture – 20 / 50 Classic Additive-Synthesis (Sinusoidal Oscillator Envelopes)
Outline
Telharmonium
Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis • Additive Analysis • Additive Synthesis
FM Synthesis
Sinusoidal Modeling
Future
John Grey 1975 — CCRMA Tech. Reports 1 & 2 (CCRMA “STANM” reports — available online)
Julius Smith Music 421 Applications Lecture – 21 / 50 Classic Additive Synthesis Diagram (Computer Music, 1960s)
Outline A1(t) f1(t) A2(t) f2(t) A3(t) f3(t) A4(t) f4(t)
Telharmonium
Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis • Additive Analysis • Additive Synthesis
FM Synthesis
Sinusoidal Modeling
Future
noise FIR Σ
4 t y(t)= Ai(t)sin ωi(t)dt + φi(0) Xi=1 Z0
Julius Smith Music 421 Applications Lecture – 22 / 50 Classic Additive-Synthesis Examples
Outline • Bb Clarinet Telharmonium • Eb Clarinet Voder • Oboe Channel Vocoder • Bassoon Phase Vocoder • Tenor Saxophone Additive Synthesis • Additive Analysis • Trumpet • Additive Synthesis • English Horn FM Synthesis • French Horn Sinusoidal Modeling • Flute Future
• All of the above • Independently synthesized set
(Synthesized from original John Grey data)
Julius Smith Music 421 Applications Lecture – 23 / 50 Outline Telharmonium Voder Channel Vocoder Phase Vocoder Additive Synthesis FM Synthesis Sinusoidal Modeling Future Frequency Modulation Synthesis (1973)
Julius Smith Music 421 Applications Lecture – 24 / 50 Frequency Modulation (FM) Synthesis
Outline FM synthesis is normally used as a spectral modeling technique Telharmonium • Voder Discovered and developed (1970s) by John M. Chowning
Channel Vocoder (CCRMA Founding Director)
Phase Vocoder • Key paper: JAES 1973 (vol. 21, no. 7)
Additive Synthesis • Commercialized by Yamaha Corporation: FM Synthesis ◦ • FM Synthesis DX-7 synthesizer (1983) • FM Formula ◦ OPL chipset (SoundBlaster PC sound card) • FM Patch • FM Spectra ◦ Cell phone ring tones • FM Examples • FM Voice • On the physical modeling front, synthesis of vibrating-string Sinusoidal Modeling waveforms using finite differences started around this time: Future Hiller & Ruiz, JAES 1971 (vol. 19, no. 6)
Julius Smith Music 421 Applications Lecture – 25 / 50 Frequency Modulation (FM) Synthesis
Outline FM synthesis is normally used as a spectral modeling technique Telharmonium • Voder Discovered and developed (1970s) by John M. Chowning
Channel Vocoder (CCRMA Founding Director)
Phase Vocoder • Key paper: JAES 1973 (vol. 21, no. 7)
Additive Synthesis • Commercialized by Yamaha Corporation: FM Synthesis ◦ • FM Synthesis DX-7 synthesizer (1983) • FM Formula ◦ OPL chipset (SoundBlaster PC sound card) • FM Patch • FM Spectra ◦ Cell phone ring tones • FM Examples • FM Voice • On the physical modeling front, synthesis of vibrating-string Sinusoidal Modeling waveforms using finite differences started around this time: Future Hiller & Ruiz, JAES 1971 (vol. 19, no. 6)
Julius Smith Music 421 Applications Lecture – 25 / 50 Frequency Modulation (FM) Synthesis
Outline FM synthesis is normally used as a spectral modeling technique Telharmonium • Voder Discovered and developed (1970s) by John M. Chowning
Channel Vocoder (CCRMA Founding Director)
Phase Vocoder • Key paper: JAES 1973 (vol. 21, no. 7)
Additive Synthesis • Commercialized by Yamaha Corporation: FM Synthesis ◦ • FM Synthesis DX-7 synthesizer (1983) • FM Formula ◦ OPL chipset (SoundBlaster PC sound card) • FM Patch • FM Spectra ◦ Cell phone ring tones • FM Examples • FM Voice • On the physical modeling front, synthesis of vibrating-string Sinusoidal Modeling waveforms using finite differences started around this time: Future Hiller & Ruiz, JAES 1971 (vol. 19, no. 6)
Julius Smith Music 421 Applications Lecture – 25 / 50 Frequency Modulation (FM) Synthesis
Outline FM synthesis is normally used as a spectral modeling technique Telharmonium • Voder Discovered and developed (1970s) by John M. Chowning
Channel Vocoder (CCRMA Founding Director)
Phase Vocoder • Key paper: JAES 1973 (vol. 21, no. 7)
Additive Synthesis • Commercialized by Yamaha Corporation: FM Synthesis ◦ • FM Synthesis DX-7 synthesizer (1983) • FM Formula ◦ OPL chipset (SoundBlaster PC sound card) • FM Patch • FM Spectra ◦ Cell phone ring tones • FM Examples • FM Voice • On the physical modeling front, synthesis of vibrating-string Sinusoidal Modeling waveforms using finite differences started around this time: Future Hiller & Ruiz, JAES 1971 (vol. 19, no. 6)
Julius Smith Music 421 Applications Lecture – 25 / 50 Frequency Modulation (FM) Synthesis
Outline FM synthesis is normally used as a spectral modeling technique Telharmonium • Voder Discovered and developed (1970s) by John M. Chowning
Channel Vocoder (CCRMA Founding Director)
Phase Vocoder • Key paper: JAES 1973 (vol. 21, no. 7)
Additive Synthesis • Commercialized by Yamaha Corporation: FM Synthesis ◦ • FM Synthesis DX-7 synthesizer (1983) • FM Formula ◦ OPL chipset (SoundBlaster PC sound card) • FM Patch • FM Spectra ◦ Cell phone ring tones • FM Examples • FM Voice • On the physical modeling front, synthesis of vibrating-string Sinusoidal Modeling waveforms using finite differences started around this time: Future Hiller & Ruiz, JAES 1971 (vol. 19, no. 6)
Julius Smith Music 421 Applications Lecture – 25 / 50 Frequency Modulation (FM) Synthesis
Outline FM synthesis is normally used as a spectral modeling technique Telharmonium • Voder Discovered and developed (1970s) by John M. Chowning
Channel Vocoder (CCRMA Founding Director)
Phase Vocoder • Key paper: JAES 1973 (vol. 21, no. 7)
Additive Synthesis • Commercialized by Yamaha Corporation: FM Synthesis ◦ • FM Synthesis DX-7 synthesizer (1983) • FM Formula ◦ OPL chipset (SoundBlaster PC sound card) • FM Patch • FM Spectra ◦ Cell phone ring tones • FM Examples • FM Voice • On the physical modeling front, synthesis of vibrating-string Sinusoidal Modeling waveforms using finite differences started around this time: Future Hiller & Ruiz, JAES 1971 (vol. 19, no. 6)
Julius Smith Music 421 Applications Lecture – 25 / 50 Frequency Modulation (FM) Synthesis
Outline FM synthesis is normally used as a spectral modeling technique Telharmonium • Voder Discovered and developed (1970s) by John M. Chowning
Channel Vocoder (CCRMA Founding Director)
Phase Vocoder • Key paper: JAES 1973 (vol. 21, no. 7)
Additive Synthesis • Commercialized by Yamaha Corporation: FM Synthesis ◦ • FM Synthesis DX-7 synthesizer (1983) • FM Formula ◦ OPL chipset (SoundBlaster PC sound card) • FM Patch • FM Spectra ◦ Cell phone ring tones • FM Examples • FM Voice • On the physical modeling front, synthesis of vibrating-string Sinusoidal Modeling waveforms using finite differences started around this time: Future Hiller & Ruiz, JAES 1971 (vol. 19, no. 6)
Julius Smith Music 421 Applications Lecture – 25 / 50 Frequency Modulation (FM) Synthesis
Outline FM synthesis is normally used as a spectral modeling technique Telharmonium • Voder Discovered and developed (1970s) by John M. Chowning
Channel Vocoder (CCRMA Founding Director)
Phase Vocoder • Key paper: JAES 1973 (vol. 21, no. 7)
Additive Synthesis • Commercialized by Yamaha Corporation: FM Synthesis ◦ • FM Synthesis DX-7 synthesizer (1983) • FM Formula ◦ OPL chipset (SoundBlaster PC sound card) • FM Patch • FM Spectra ◦ Cell phone ring tones • FM Examples • FM Voice • On the physical modeling front, synthesis of vibrating-string Sinusoidal Modeling waveforms using finite differences started around this time: Future Hiller & Ruiz, JAES 1971 (vol. 19, no. 6)
Julius Smith Music 421 Applications Lecture – 25 / 50 FM Formula
Outline
Telharmonium x(t)= Ac sin[ωct + φc + Am sin(ωmt + φm)] Voder where Channel Vocoder
Phase Vocoder (Ac,ωc,φc) specify the carrier sinusoid Additive Synthesis (Am,ωm,φm) specify the modulator sinusoid
FM Synthesis • FM Synthesis Can also be called phase modulation • FM Formula • FM Patch • FM Spectra • FM Examples • FM Voice
Sinusoidal Modeling
Future
Julius Smith Music 421 Applications Lecture – 26 / 50 Simple FM “Brass” Patch (Chowning 1970–)
Jean-Claude Risset observation (1964–1969): Outline Brass bandwidth ∝ amplitude Telharmonium
Voder
Channel Vocoder
Phase Vocoder fm = f0 Additive Synthesis g FM Synthesis • FM Synthesis A F • FM Formula • FM Patch • FM Spectra • FM Examples fc = f0 • FM Voice
Sinusoidal Modeling Future A F
Out
Julius Smith Music 421 Applications Lecture – 27 / 50 FM Harmonic Amplitudes (Bessel Function of First Kind)
Outline Harmonic number k, FM index β:
Telharmonium
Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis
FM Synthesis 1 • FM Synthesis • FM Formula • FM Patch 0.5 • FM Spectra )
• FM Examples β ( k • FM Voice J 0 Sinusoidal Modeling 0
Future 2 −0.5 4 0 5 10 6 15 20 8 25 Order k 30 10 Argument β
Julius Smith Music 421 Applications Lecture – 28 / 50 Frequency Modulation (FM) Examples
All examples by John Chowning unless otherwise noted: Outline Telharmonium • FM brass synthesis Voder • Channel Vocoder Low Brass example
Phase Vocoder • Dexter Morril’s FM Trumpet Additive Synthesis • FM singing voice (1978) FM Synthesis • FM Synthesis Each formant synthesized using an FM operator pair • FM Formula (two sinusoidal oscillators) • FM Patch • FM Spectra • Chorus • FM Examples • FM Voice • Voices
Sinusoidal Modeling • Basso Profundo Future • Other early FM synthesis • Clicks and Drums • Big Bell • String Canon
Julius Smith Music 421 Applications Lecture – 29 / 50 FM Voice
Outline FM voice synthesis can be viewed as compressed modeling of Telharmonium spectral formants Voder
Channel Vocoder Carrier 2 Phase Vocoder Carrier 1 Carrier 3 Additive Synthesis
FM Synthesis • FM Synthesis • FM Formula
• FM Patch Magnitude • FM Spectra • FM Examples • FM Voice 0 Frequency f Sinusoidal Modeling Modulation Frequency (all three) Future
Julius Smith Music 421 Applications Lecture – 30 / 50 Outline Telharmonium Voder Channel Vocoder Phase Vocoder Additive Synthesis FM Synthesis Sinusoidal Modeling Future Sinusoidal Modeling Synthesis (1988)
Julius Smith Music 421 Applications Lecture – 31 / 50 Tracking Spectral Peaks in the Short-Time Fourier Transform
Outline Phases Telharmonium atan
Voder s(t) Channel Vocoder FFT Frequencies Phase Vocoder Quadratic Peak Additive Synthesis dB mag Peak tracking Interpolation FM Synthesis window w(n) Amplitudes Sinusoidal Modeling • Sinusoidal Modeling • Spectral Trajectories • Sines + Noise • S+N Examples • STFT peak tracking at CCRMA: mid-1980s (PARSHL program) • S+N FX • S+N XSynth • Sines + Transients • Motivated by vocoder analysis of piano tones • S + N + Transients • • S+N+T TSM Influences: STFT (Allen and Rabiner 1977), • S+N+T Freq Map ADEC (1977), MAPLE (1979) • S+N+T Windows • HF Noise Modeling • Independently developed for speech coding by McAulay and • HF Noise Band Quatieri at Lincoln Labs (1985) • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 32 / 50 Example Spectral Trajectories
Outline f Telharmonium
Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis
FM Synthesis
Sinusoidal Modeling • Sinusoidal Modeling • Spectral Trajectories • Sines + Noise • S+N Examples • S+N FX • S+N XSynth • Sines + Transients • S + N + Transients t • S+N+T TSM • S+N+T Freq Map • S+N+T Windows • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 33 / 50 Parametric Spectral Modeling
1 1 2 2 3 3 4 4 Outline A (t) f (t) A (t) f (t) A (t) f (t) A (t) f (t)
Telharmonium
Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis
FM Synthesis
Sinusoidal Modeling • Sinusoidal Modeling • Spectral Trajectories • Sines + Noise • S+N Examples • S+N FX • S+N XSynth white noise • filter(t) Sines + Transients u(t) • S + N + Transients ht(τ) • S+N+T TSM P • S+N+T Freq Map • S+N+T Windows 4 • HF Noise Modeling t i i i t ∗ • HF Noise Band y(t)= A (t)cos 0 ω (t)dt + φ (0) +(h u)(t) i=1 • S+N+T Examples P hR i Future Julius Smith Music 421 Applications Lecture – 34 / 50 Sines + Noise Sound Examples
Outline Xavier Serra thesis demos (Sines + Noise signal modeling) Telharmonium • Voder Piano Channel Vocoder ◦ Original Phase Vocoder ◦ Sinusoids alone Additive Synthesis ◦ Residual after sinusoids removed FM Synthesis ◦ Sines + noise model Sinusoidal Modeling • Sinusoidal Modeling • Voice • Spectral Trajectories • Sines + Noise ◦ • S+N Examples Original • S+N FX ◦ Sinusoids • S+N XSynth ◦ • Sines + Transients Residual • S + N + Transients ◦ Synthesis • S+N+T TSM • S+N+T Freq Map • S+N+T Windows • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 35 / 50 Musical Effects with Sines+Noise Models
Outline • Piano Effects Telharmonium ◦ Voder Pitch downshift one octave ◦ Channel Vocoder Pitch flattened
Phase Vocoder ◦ Varying partial stretching Additive Synthesis • Voice Effects FM Synthesis
Sinusoidal Modeling ◦ Frequency-scale by 0.6 • Sinusoidal Modeling ◦ Frequency-scale by 0.4 and stretch partials • Spectral Trajectories • Sines + Noise ◦ Variable time-scaling, deterministic to stochastic • S+N Examples • S+N FX • S+N XSynth • Sines + Transients • S + N + Transients • S+N+T TSM • S+N+T Freq Map • S+N+T Windows • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 36 / 50 Cross-Synthesis with Sines+Noise Models
Outline • Voice “modulator” Telharmonium Voder • Creaking ship’s mast “carrier” Channel Vocoder • Voice-modulated creaking mast Phase Vocoder • Same with modified spectral envelopes Additive Synthesis
FM Synthesis
Sinusoidal Modeling • Sinusoidal Modeling • Spectral Trajectories • Sines + Noise • S+N Examples • S+N FX • S+N XSynth • Sines + Transients • S + N + Transients • S+N+T TSM • S+N+T Freq Map • S+N+T Windows • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 37 / 50 Sines + Transients Sound Examples
Outline In this technique, the sinusoidal sum is phase-matched at the Telharmonium cross-over point only (with no cross-fade). Voder
Channel Vocoder • Marimba
Phase Vocoder ◦ Original Additive Synthesis ◦ Sinusoidal model FM Synthesis ◦ Sinusoidal Modeling Original attack, followed by sinusoidal model • Sinusoidal Modeling • Spectral Trajectories • Piano • Sines + Noise • S+N Examples ◦ Original • S+N FX ◦ Sinusoidal model • S+N XSynth • Sines + Transients ◦ Original attack, followed by sinusoidal model • S + N + Transients • S+N+T TSM • S+N+T Freq Map • S+N+T Windows • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 38 / 50 Multiresolution Sines + Noise + Transients
Outline Why Model Transients Separately? Telharmonium
Voder • Sinusoids efficiently model spectral peaks over time Channel Vocoder • Filtered noise efficiently models spectral residual vs. t Phase Vocoder • Neither is good for abrupt transients in the waveform Additive Synthesis • Phase-matched oscillators are expensive FM Synthesis • More efficient to switch to a transient model during transients Sinusoidal Modeling • • Sinusoidal Modeling Need sinusoidal phase matching at the switching times • Spectral Trajectories • Sines + Noise Transient models: • S+N Examples • S+N FX • S+N XSynth • Original waveform slice (1988) • Sines + Transients • • S + N + Transients Wavelet expansion (Ali 1996) • S+N+T TSM • MPEG-2 AAC (with short window) (Levine 1998) • S+N+T Freq Map • • S+N+T Windows Frequency-domain LPC • HF Noise Modeling (time-domain amplitude envelope) (Verma 2000) • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 39 / 50 Time Scale Modification of Sines + Noise + Transients Models
Outline transients transients sines + sines + sines + Telharmonium original signal noise noise noise Voder
Channel Vocoder
Phase Vocoder
Additive Synthesis transients transients time-scaled sines + sines + sines + FM Synthesis signal noise noise noise Sinusoidal Modeling • Sinusoidal Modeling • Spectral Trajectories • Sines + Noise time • S+N Examples • S+N FX • S+N XSynth Time-Scale Modification (TSM) becomes well defined: • Sines + Transients • S + N + Transients • Transients are translated in time • S+N+T TSM • S+N+T Freq Map • Sinusoidal envelopes are scaled in time • S+N+T Windows • • HF Noise Modeling Noise-filter envelopes also scaled in time • HF Noise Band • Dual of TSM is frequency scaling • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 40 / 50 Sines + Noise + Transients Time-Frequency Map
16 Outline 14 Telharmonium 12 Voder
Channel Vocoder 10
Phase Vocoder 8
Additive Synthesis 6 frequency [kHz] FM Synthesis 4
Sinusoidal Modeling 2 • Sinusoidal Modeling • 0 Spectral Trajectories 0 50 100 150 200 250 • Sines + Noise 1 • S+N Examples 0.5 • S+N FX • S+N XSynth 0 • Sines + Transients amplitude • S + N + Transients −0.5 • S+N+T TSM −1 • S+N+T Freq Map 0 50 100 150 200 250 time [milliseconds] • S+N+T Windows • HF Noise Modeling (Levine 1998) • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 41 / 50 Corresponding Analysis Windows
Outline
Telharmonium transient Voder
Channel Vocoder
Phase Vocoder high octave Additive Synthesis
FM Synthesis
Sinusoidal Modeling
• Sinusoidal Modeling middle octave • Spectral Trajectories • Sines + Noise • S+N Examples low octave • S+N FX • S+N XSynth • Sines + Transients • S + N + Transients • S+N+T TSM • S+N+T Freq Map • S+N+T Windows amplitude • HF Noise Modeling • HF Noise Band 0 50 100 150 200 250 • S+N+T Examples time [milliseconds]
Future Julius Smith Music 421 Applications Lecture – 42 / 50 Quasi-Constant-Q (Wavelet) Time-Frequency Map
16 Outline 14 Telharmonium 12 Voder
Channel Vocoder 10
Phase Vocoder 8
Additive Synthesis 6 frequency [kHz] FM Synthesis 4
Sinusoidal Modeling 2 • Sinusoidal Modeling • Spectral Trajectories 0 0 4 50 100 150 200 250 • Sines + Noise x 10 • S+N Examples 2 • S+N FX 1 • S+N XSynth 0 • Sines + Transients
• S + N + Transients amplitude −1 • S+N+T TSM −2 • S+N+T Freq Map 0 50 100 150 200 250 • S+N+T Windows time [milliseconds] • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 43 / 50 Bark-Band Noise Modeling at High Frequencies (Levine 1998)
Outline 85
Telharmonium 80 Voder
Channel Vocoder 75
Phase Vocoder 70 Additive Synthesis 65 FM Synthesis
Sinusoidal Modeling 60 • Sinusoidal Modeling • Spectral Trajectories 55 • Sines + Noise magnitude [dB] • S+N Examples 50 • S+N FX • S+N XSynth 45 • Sines + Transients • S + N + Transients 40 • S+N+T TSM • S+N+T Freq Map 35 • S+N+T Windows • HF Noise Modeling 30 • 0 500 1000 1500 2000 2500 3000 3500 4000 4500 HF Noise Band frequency [Hz] • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 44 / 50 Amplitude Envelope for One Noise Band
Outline 80
Telharmonium 70 Voder 60 Channel Vocoder
Phase Vocoder 50 Original Mag. [dB] Additive Synthesis 40 FM Synthesis 0 50 100 150 200 250 300 350
Sinusoidal Modeling • Sinusoidal Modeling 80 • Spectral Trajectories 75 • Sines + Noise 70 • S+N Examples 65 • S+N FX 60 • S+N XSynth 55 • Sines + Transients LSA Mag. [dB] • S + N + Transients 50 • S+N+T TSM 45 • 0 50 100 150 200 250 300 350 S+N+T Freq Map time [milliseconds] • S+N+T Windows • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 45 / 50 Sines + Noise + Transients Sound Examples
Outline Scott Levine Thesis Demos (Sines + Noise + Transients at 32 kbps) Telharmonium (http://ccrma.stanford.edu/~scottl/thesis.html) Voder
Channel Vocoder
Phase Vocoder Additive Synthesis “It Takes Two” by Rob Base & DJ E-Z Rock FM Synthesis
Sinusoidal Modeling • Original • Sinusoidal Modeling • MPEG-AAC at 32 kbps • Spectral Trajectories • Sines + Noise • Sines+transients+noise at 32 kbps • S+N Examples • S+N FX • S+N XSynth • Multiresolution sinusoids • Sines + Transients • S + N + Transients • Residual Bark-band noise • S+N+T TSM • Transform-coded transients (AAC) • S+N+T Freq Map • S+N+T Windows • Bark-band noise above 5 kHz • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 46 / 50 Time Scale Modification using Sines + Noise + Transients
Outline Scott Levine Thesis Demos (Sines + Noise + Transients at 32 kbps) Telharmonium (http://ccrma.stanford.edu/~scottl/thesis.html) Voder
Channel Vocoder
Phase Vocoder Additive Synthesis Time-Scale Modification (pitch unchanged) FM Synthesis • S+N+T time-scale factors [2.0, 1.6, 1.2, 1.0, 0.8, 0.6, 0.5] Sinusoidal Modeling • Sinusoidal Modeling • Spectral Trajectories • Sines + Noise • S+N Examples S+N+T Pitch Shifting (timing unchanged) • S+N FX • S+N XSynth • Pitch-scale factors [0.89, 0.94, 1.00, 1.06, 1.12] • Sines + Transients • S + N + Transients • S+N+T TSM • S+N+T Freq Map • S+N+T Windows • HF Noise Modeling • HF Noise Band • S+N+T Examples
Future Julius Smith Music 421 Applications Lecture – 47 / 50 Outline Telharmonium Voder Channel Vocoder Phase Vocoder Additive Synthesis FM Synthesis Sinusoidal Modeling Future Summary and Future Prospects
Julius Smith Music 421 Applications Lecture – 48 / 50 Spectral Modeling History Highlights
• Bernoulli’s modal sums (1733) Perceptual audio coding: • Fourier’s initial theorem (1822) • Princen-Bradley filterbank • Telharmonium (1906) (1986) • Hammond organ (1930s) • K. Brandenburg thesis (1989) • Channel Vocoder (1939) • Auditory masking usage • Phase Vocoder (1966) • Dolby AC2 • “Additive Synthesis” (1969) • Musicam • FFT Phase Vocoder (1976) • ASPEC • Sinusoidal Modeling • MPEG-I,II,IV (1977,1979,1985) (S+N+T “parametric sounds”) • Sines+Noise (1989) • Sines+Transients (1989) • TF Reassignment (1995) • Sines+Noise+Transients (1998)
Julius Smith Music 421 Applications Lecture – 49 / 50 Future Prospects
Observations: • Sinusoidal modeling of sound is “Unreasonably Effective” • Basic “auditory masking” discards ≈ 90% information • Interesting neuroscience observation: “... most neurons in the primary auditory cortex A1 are silent most of the time ...” (from “Sparse Time-Frequency Representations”, Gardner and Magnesco, PNAS:103(16), April 2006) • What is the right “psychospectral model” for sound? ◦ The cochlea of the ear is a real-time spectrum analyzer ◦ How is the “ear’s spectrogram” represented at higher levels?
Julius Smith Music 421 Applications Lecture – 50 / 50 Future Prospects
Observations: • Sinusoidal modeling of sound is “Unreasonably Effective” • Basic “auditory masking” discards ≈ 90% information • Interesting neuroscience observation: “... most neurons in the primary auditory cortex A1 are silent most of the time ...” (from “Sparse Time-Frequency Representations”, Gardner and Magnesco, PNAS:103(16), April 2006) • What is the right “psychospectral model” for sound? ◦ The cochlea of the ear is a real-time spectrum analyzer ◦ How is the “ear’s spectrogram” represented at higher levels?
Julius Smith Music 421 Applications Lecture – 50 / 50 Future Prospects
Observations: • Sinusoidal modeling of sound is “Unreasonably Effective” • Basic “auditory masking” discards ≈ 90% information • Interesting neuroscience observation: “... most neurons in the primary auditory cortex A1 are silent most of the time ...” (from “Sparse Time-Frequency Representations”, Gardner and Magnesco, PNAS:103(16), April 2006) • What is the right “psychospectral model” for sound? ◦ The cochlea of the ear is a real-time spectrum analyzer ◦ How is the “ear’s spectrogram” represented at higher levels?
Julius Smith Music 421 Applications Lecture – 50 / 50 Future Prospects
Observations: • Sinusoidal modeling of sound is “Unreasonably Effective” • Basic “auditory masking” discards ≈ 90% information • Interesting neuroscience observation: “... most neurons in the primary auditory cortex A1 are silent most of the time ...” (from “Sparse Time-Frequency Representations”, Gardner and Magnesco, PNAS:103(16), April 2006) • What is the right “psychospectral model” for sound? ◦ The cochlea of the ear is a real-time spectrum analyzer ◦ How is the “ear’s spectrogram” represented at higher levels?
Julius Smith Music 421 Applications Lecture – 50 / 50 Future Prospects
Observations: • Sinusoidal modeling of sound is “Unreasonably Effective” • Basic “auditory masking” discards ≈ 90% information • Interesting neuroscience observation: “... most neurons in the primary auditory cortex A1 are silent most of the time ...” (from “Sparse Time-Frequency Representations”, Gardner and Magnesco, PNAS:103(16), April 2006) • What is the right “psychospectral model” for sound? ◦ The cochlea of the ear is a real-time spectrum analyzer ◦ How is the “ear’s spectrogram” represented at higher levels?
Julius Smith Music 421 Applications Lecture – 50 / 50 Future Prospects
Observations: • Sinusoidal modeling of sound is “Unreasonably Effective” • Basic “auditory masking” discards ≈ 90% information • Interesting neuroscience observation: “... most neurons in the primary auditory cortex A1 are silent most of the time ...” (from “Sparse Time-Frequency Representations”, Gardner and Magnesco, PNAS:103(16), April 2006) • What is the right “psychospectral model” for sound? ◦ The cochlea of the ear is a real-time spectrum analyzer ◦ How is the “ear’s spectrogram” represented at higher levels?
Julius Smith Music 421 Applications Lecture – 50 / 50 Future Prospects
Observations: • Sinusoidal modeling of sound is “Unreasonably Effective” • Basic “auditory masking” discards ≈ 90% information • Interesting neuroscience observation: “... most neurons in the primary auditory cortex A1 are silent most of the time ...” (from “Sparse Time-Frequency Representations”, Gardner and Magnesco, PNAS:103(16), April 2006) • What is the right “psychospectral model” for sound? ◦ The cochlea of the ear is a real-time spectrum analyzer ◦ How is the “ear’s spectrogram” represented at higher levels?
Julius Smith Music 421 Applications Lecture – 50 / 50