### Digital Filter Models of Damped Strings

In an efficient digital simulation, lumped loss factors of the form are approximated by a rational frequency response . In general, the coefficients of the optimal rational loss filter are obtained by minimizing with respect to the filter coefficients or the poles and zeros of the filter. To avoid introducing frequency-dependent delay, the loss filter should be a*zero-phase, finite-impulse-response*(FIR) filter [362]. Restriction to zero phase requires the impulse response to be finite in length (

*i.e.*, an FIR filter) and it must be symmetric about time zero,

*i.e.*, . In most implementations, the zero-phase FIR filter can be converted into a causal,

*linear phase*filter by reducing an adjacent delay line by half of the impulse-response duration.

**Next Section:**

Lossy Finite Difference Recursion

**Previous Section:**

Well Posed PDEs for Modeling Damped Strings