A History of Spectral Audio Signal Processing

This appendix surveys some of the highlights of developments in spectral audio signal processing, beginning with Daniel Bournoulli's original understanding of acoustic vibration as a superposition of sinusoidally vibrating modes and progressing through recent history in spectral modeling, with emphasis on sinusoidal models.

Our historical tour will touch upon the following milestones in audio spectral modeling:

• Bernoulli's understanding of superimposed sinusoidal vibrations (1733)
• Fourier's theorem (1822)
• Helmholtz's understanding of the ear as a spectrum analyzer (1863)
• Telharmonium (1898)
• Hammond Organ (1934)
• Vocoder (1935)
• Voder (1937)
• Phase Vocoder (1966)
• Additive Synthesis in computer music (1969)
• FM Brass Synthesis (1970)
• Synclavier 8-bit FM/Additive synthesizer (1975)
• FM singing voice (1978)
• Sinusoidal Modeling (1977,1979,1985)
• Sines + Noise (1988)
• Sines + Noise + Transients (1988,1996,1998,2000)
• MPEG-style Audio Compression (1986-present)

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Subsections

• Daniel Bernoulli's Modal Decomposition
• The Telharmonium
• Early Additive Synthesis in Film Making
• The Hammond Organ
• Dudley's Channel Vocoder
• Voder
• Phase Vocoder
  • FFT Implementation of the Phase Vocoder
  • Phase Vocoder Applications
  
  
• Additive Synthesis
  • Oscillator-Bank Resynthesis
  • Inverse FFT Synthesis
  • Chirplet Synthesis
  • Nonparametric Spectral Peak Modeling
  • Efficient Specialized Methods
    • Wavetable Synthesis
    • Group-Additive Synthesis
  • Further Reading, Additive Synthesis
  
  
• Frequency Modulation (FM) Synthesis
  • FM Harmonic Amplitudes
  • FM Brass
  • FM Voice
    • Further Reading about FM Synthesis
  
  
• Phase Vocoder Sinusoidal Modeling
  • Computing Vocoder Parameters
    • Frequency Envelopes
    • Envelope Compression
    • Vocoder-Based Additive-Synthesis Limitations
  • Further Reading on Vocoders
  
  
• Speech Synthesis Examples
• Spectral Modeling Synthesis
  • Short Time Fourier Analysis/Modification/Resynthesis
  • Sinusoidal Modeling Systems
  • Inverse FFT Synthesis
  • Sines+Noise Synthesis
  • Multiresolution Sinusoidal Modeling
  • Transient Models
  • S+N+T Sound Examples
  • Time-Frequency Reassignment
  • Perceptual Audio Compression
  • TSM of Sinusoidal Models
  • Further Reading
  
  
• Perceptual audio coding
• Future Prospects

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Next: Daniel Bernoulli's Modal Decomposition

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.