Loop Filter Identification

In §6.7 we discussed damping filters for vibrating string models, and in §6.9 we discussed dispersion filters. For vibrating strings, which are well described by a linear time-invariant (LTI) partial differential equation, damping and dispersion filtering are the only deviations possible from the ideal string discussed in §6.1.

The ideal damping filter is ``zero phase'' (or linear phase)
[452],^{7.10}while the ideal dispersion filter is ``allpass'' (as described in
§6.9.1). Since
every desired frequency response can be decomposed into a zero-phase
frequency-response in series with an allpass frequency-response, we
may design a single loop filter whose amplitude response gives the
desired damping as a function of frequency, and whose phase response
gives the desired dispersion vs. frequency. The next subsection
summarizes some methods based on this approach. The following two
subsections discuss methods for the design of damping and dispersion
filters separately.

- General Loop-Filter Design
- Damping Filter Design
- Dispersion Filter Design
- Fundamental Frequency Estimation

- EDR-Based Loop-Filter Design

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