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Contents
Foreword
Preface
Sinusoids, amplitude and frequency
Measures of Amplitude
Units of Amplitude
Controlling Amplitude
Frequency
Synthesizing a sinusoid
Superposing Signals
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
More additive synthesis
Exercises
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
Exercises
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
Audio signals as control
Operations on control streams
Control operations in Pd
Examples
Sampling and foldover
Converting controls to signals
Non-looping wavetable player
Signals to controls
Analog-style sequencer
MIDI-style synthesizer
Exercises
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
Exercises
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
Exercises
Designer spectra
Carrier/modulator model
Pulse trains
Pulse trains via waveshaping
Pulse trains via wavetable stretching
Resulting spectra
Movable ring modulation
Phase-aligned formant (PAF) generator
Examples
Wavetable pulse train
Simple formant generator
Two-cosine carrier signal
The PAF generator
Stretched wavetables
Exercises
Time shifts and delays
Complex numbers
Complex sinusoids
Time shifts and phase changes
Delay networks
Recirculating delay networks
Power conservation and complex delay networks
Artificial reverberation
Controlling reverberators
Variable and fractional shifts
Fidelity 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
Elementary filters
Elementary non-recirculating filter
Non-recirculating filter, second form
Elementary recirculating filter
Compound filters
Real outputs from complex filters
Two recirculating filters for the price of one
Designing filters
One-pole low-pass filter
One-pole, one-zero high-pass filter
Shelving filter
Band-pass filter
Peaking and stop-band 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-varying band-pass filter
Envelope followers
Single sideband modulation
Using elementary filters directly: shelving and peaking
Making and using all-pass filters
Exercises
Fourier analysis and resynthesis
Fourier analysis of periodic signals
Periodicity of the Fourier transform
Fourier transform as additive synthesis
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
Exercises
Classical waveforms
Symmetries and Fourier series
Sawtooth waves and symmetry
Dissecting classical waveforms
Fourier series of the elementary waveforms
Sawtooth wave
Parabolic wave
Square and symmetric triangle waves
General (non-symmetric) triangle wave
Predicting and controlling foldover
Over-sampling
Sneaky triangle waves
Transition splicing
Examples
Combining sawtooth waves
Strategies for band-limiting sawtooth waves
Exercises
Index
Bibliography
About this document ...
Miller Puckette 2006-12-30