Loop Filter Identification

In §4.6 we discussed damping filters for vibrating string models, and in §4.8 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 string discussed in §4.1.

The ideal damping filter is ``zero phase'' (or linear phase) [460],<sup>5.12</sup>while the ideal dispersion filter is ``allpass'' (as described in §4.8.1). Since every desired frequency responds 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.

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Subsections

• General Loop-Filter Design
• Damping Filter Design
• Dispersion Filter Design
• Fundamental Frequency Estimation
  • Approximate Maximum Likelihood F0 Estimation
  • References on F0 Estimation
  • Extension to Stiff Strings
  
  
• EDR-Based Loop-Filter Design

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.