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Substituting finite difference approximation (FDA)
into the wave equation
gives
Time Update:
Let
(speed of sound along the string).
In practice, we typically normalize such that
- Higher order wave equations yield more terms of the form
frequency-dependent losses and/or dispersion
characteristics are introduced into the FDA:
- Linear differential equations with constant coefficients give rise to some
linear, time-invariant discrete-time system via the FDA
- Linear, time-invariant, ``filtered waveguide'' case:
- More general linear, time-invariant case
- Nonlinear example:
- Time-varying example:
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