Contents

• Introduction
• Acoustics of digital audio signals
  • Measures of Amplitude
  • Amplitude of Combined Signals
  • Units of Amplitude
  • Controlling Amplitude
  • Synthesizing a Sinusoid
  • Superposing Sinusoids
  • Frequency
  • Periodic Signals
  • About the Software Examples
    • Quick Introduction to Pd
    • How to find and run the examples
  • Examples
    • constant amplitude scaler
    • amplitude control in decibels
    • smoothed amplitude control with an envelope generator
    • major triad
    • conversion between frequency and pitch
  
  
• Wavetables and samplers
  • The Wavetable Oscillator
  • Sampling
  • Enveloping samplers
  • Timbre stretching
  • Interpolation
  • Examples
    • wavetable oscillator
    • wavetable lookup in general
    • using a wavetable as a sampler
    • looping samplers
    • Overlapping sample looper
    • Automatic read point precession
  
  
• Audio and control computations
  • The sampling theorem
  • Control
  • Control streams
  • Converting from audio signals to numeric control streams
  • Control streams in block diagrams
  • Event detection
  • Control computation using audio signals directly
  • Operations on control streams
  • Control operations in Pd
  • Examples
    • Sampling and foldover
    • Converting controls to signals
    • Non-looping sample player
    • Signals to controls
    • Analog-style sequencer
    • MIDI-style synthesizer
  
  
• Automation and voice management
  • Envelope Generators
  • Linear and Curved Amplitude Shapes
  • Continuous and discontinuous control changes
    • Muting
    • Switch-and-ramp
  • Polyphony
  • Voice allocation
  • Voice tags
  • Encapsulation in Pd
  • Examples
    • ADSR envelope generator
    • Transfer functions for amplitude control
    • Additive synthesis: Risset's bell
    • Additive synthesis: spectral envelope control
    • Polyphonic synthesis: sampler
  
  
• Modulation
  • Taxonomy of spectra
  • Multiplying audio signals
  • Waveshaping
  • Frequency and phase modulation
  • Examples
    • Ring modulation and spectra
    • Octave divider and formant adder
    • Waveshaping and difference tones
    • Waveshaping using Chebychev polynomials
    • Waveshaping using an exponential function
    • Sinusoidal waveshaping: evenness and oddness
    • Phase modulation and FM
  
  
• Designer spectra
  • Carrier/modulator model
  • Pulse trains
  • Movable ring modulation
  • Phase-aligned formant (PAF) generator
  • Examples
    • Wavetable pulse train
    • Simple formant generator
    • Two-cosine carrier signal
    • The PAF generator
  
  
• Time shifts
  • Complex numbers
    • Sinusoids as geometric series
  • Time shifts and phase changes
  • Delay networks
  • Recirculating delay networks
  • Power conservation and complex delay networks
  • Artificial reverberation
    • Controlling reverberators
  • Variable and fractional shifts
  • Accuracy and frequency response of interpolating delay lines
  • Pitch shifting
  • Examples
    • Fixed, noninterpolating delay line
    • Recirculating comb filter
    • Variable delay line
    • Order of execution and lower limits on delay times
    • Order of execution in non-recirculating delay lines
    • Non-recirculating comb filter as octave doubler
    • Time-varying complex comb filter: shakers
    • Reverberator
    • Pitch shifter
    • Exercises
  
  
• Filters
  • Taxonomy of filters
    • Low-pass and high-pass filters
    • Band-pass and stop-band filters
    • Equalizing filters
  • Designing filters
    • Elementary non-recirculating filter
    • Non-recirculating filter, second form
    • Elementary recirculating filter
    • Compound filters
    • Real outputs from complex filters
  • Designing filters
    • One-pole low-pass filter
    • One-pole, one-zero high-pass filter
    • Shelving filter
    • Band-pass filter
    • Peaking and band-stop filter
    • Butterworth filters
    • Stretching the unit circle with rational functions
    • Butterworth band-pass filter
    • Time-varying coefficients
    • Impulse responses of recirculating filters
    • All-pass filters
  • Applications
    • Subtractive synthesis
    • Envelope following
    • Single Sideband Modulation
  • Examples
    • Prefabricated low-, high-, and band-pass filters
    • Prefabricated time-variable band-pass filter
    • Envelope followers
    • Single sideband modulation
    • Using elementary filters directly: shelving and peaking
    • Making and using all-pass filters
  
  
• Fourier analysis and resynthesis
  • Fourier analysis of periodic signals
    • Fourier transform as additive synthesis
    • Periodicity of the Fourier transform
  • Properties of Fourier transforms
    • Fourier transform of DC
    • Shifts and phase changes
    • Fourier transform of a sinusoid
  • Fourier analysis of non-periodic signals
  • Fourier analysis and reconstruction of audio signals
    • Narrow-band companding
    • Timbre stamping (classical vocoder)
  • Phase
    • Phase relationships between channels
  • Phase bashing
  • Examples
    • Fourier analysis and resynthesis in Pd
    • Narrow-band companding: noise suppression
    • Timbre stamp (``vocoder")
    • Phase vocoder time bender
  
  
• Index
• Bibliography