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- Recall:
- Position
is eliminated from the simulation
- Position
remains laid out from left to right
- Left- and right-going traveling waves must be summed to produce a
physical output
- Similar to ladder and lattice digital filters
Important point: Discrete time simulation is exact at the
sampling instants, to within the numerical precision of the samples
themselves.
To avoid aliasing associated with sampling:
- Require all initial waveshapes be bandlimited to
- Require all external driving signals be similarly bandlimited
- Avoid nonlinearities or keep them ``weak''
- Avoid time variation or keep it slow
- Use plenty of oversampling and lowpass filtering with rapid
high-frequency roll-off in severely nonlinear and/or time-varying
cases
- Prefer ``feed-forward'' over ``feed-back'' around nonlinearities
and/or modulations when possible
Interactive simulation of a vibrating string:
http://www.colorado.edu/physics/phet/simulations/stringwave/stringWave.swf
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Download StringWaves.pdf
Download StringWaves_2up.pdf
Download StringWaves_4up.pdf