Physical modeling

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Physical modelingExcitation and resonanceTypesMass-spring paradigmModal synthesisDigital waveguidesFormant synthesisStochastic synthesisExamplesReferences
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Physical modeling
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Excitation and resonance
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Physical modeling is a the construction of a system that resonates when it is excited (very much like a real intrument)
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Output is the system's state sampled at a particular location
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Types
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Mass-spring paradigm
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Modal synthesis
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A sound object is modeled as a collection of vibrating sub-structures
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Less structures to compute than the mass-spring system
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Each substructure has
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a set of frequencies and damping coefficients for the substructure's resonating nodes
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coordinates describing the mode's shape
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Allows combining different sub-structures together to create new instruments
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Can be estimated and computed from geometric and material modeling
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Often calculated from measurements of objects
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Often modeled in with biquad resonators
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Digital waveguides
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Discrete Realization of the 1D wave equation,
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A superposition of a right-going and left going wave
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en.wikipedia.org > Wiki > Digital waveguide synthesis User Link
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Digital delay lines to model the traveling of waves
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Digital filters to represent the losses at the string and the boundaries
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Often non-linear elements are added
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Membranes can be modeled as 2d waveguide meshes and Reverb can be modeles as 3D waveguide meshes
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Julius O. Smith
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Banded waveguides
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Georg Essl and Perry Cook
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Each frequency band is modeled using a different waveguide, to model the frequency dependent behavior of propagation and resonance of objects
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Karplus-Strong algorithm
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Fill a filtered delay line with random numbers
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Jaffe-Smith extension
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Greater control of decay time
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Improves tuning problems
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https://ccrma.stanford.edu/~jos/pasp/Extended_Karplus_Strong_Algorithm.html User Link
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Model the movement of energy across vibrating bodies (strings/tubes)
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Formant synthesis
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Generally a source-filter model
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Like voiced speech
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The source is the glottal pulse train
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The filter is the vocal tract (tounge and mouth)
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FOF/ VOSIM
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The pulse+filter is simplified by producing time decaying sinusoids
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Used for singing voice
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Stochastic synthesis
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Modelling processes which are random
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e.g. seeds in a maraca, footsteps on sand
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Generally using modal synthesis or granular synthesis
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Examples
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Guitar
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https://soundcloud.com/spicyguitar User Link
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spicyguitar.com User Link
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acoustics.hut.fi > Demos User Link
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Keyboards
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applied-acoustics.com > Modelingcollection > Overview User Link
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pianoteq User Link
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www.physispiano.com
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Woodwinds
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https://ccrma.stanford.edu/software/stk/ User Link
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Percussion
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Orchestral
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synful.com User Link
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References
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https://ccrma.stanford.edu/~jos/pasp/pasp.html User Link
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Good intro in C. Roads "The Computer Music Tutorial"
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Perry Cook. Real Sound Synthesis for Interactive Applications