General Loop-Filter DesignFor general loop-filter design in vibrating string models (as well as in woodwind and brass instrument bore models), we wish to minimize [428, pp. 182-184]: filter's amplitude response, while the partial tunings are determined by the filter's phase response. There also may be other filters in the loop (such as a delay-line interpolation filter) which need to be considered when designing the main loop filter.
There are numerous methods for designing the string loop filter based on measurements of real string behavior. In , a variety of methods for system identification  were explored for this purpose, including ``periodic linear prediction'' in which a linear combination of a small group of samples is used to predict a sample one period away from the midpoint of the group. An approach based on a genetic algorithm is described in ; in that work, the error measure used with the genetic algorithm is based on properties of human perception of short-time spectra, as is now standard practice in digital audio coding . Overviews of other approaches appear in  and . Below is an outline of a simple and effective method used (ca. 1995) to design loop filters for some of the Sondius sound examples:
- Estimate the fundamental frequency (see §6.11.4 below)
- Set a Hamming FFT-window length to approximately four periods
- Compute the short-time Fourier transform (STFT)
- Perform a sinusoidal modeling analysis  to
- detect peaks in each spectral frame, and
- connect peaks through time to form amplitude envelopes
- Fit an exponential to each amplitude envelope
- Prepare the desired frequency-response, sampled at the harmonic
frequencies of the delay-line loop without the loop filter. At
each harmonic frequency,
- the nearest-partial decay-rate gives the desired loop-filter gains,
- the nearest-partial peak-frequency give the desired loop-filter phase delay.
- Use a phase-sensitive filter-design method such as invfreqz in matlab to design the desired loop filter from its frequency-response samples (further details below).
Damping Filter Design