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Damping Filter Design

When dispersion can be neglected (as it typically can in many cases, such as for guitar strings), we may use linear-phase filter design methods, such as provided by the functions remez, firls, and fir2 in matlab. Since strings are usually very lightly damped, such linear-phase filter designs give high quality at very low orders. Another approach is to fit a low-order IIR filter, such as by applying invfreqz to a minimum-phase version of the desired amplitude response, and then subtract the phase-response of the resulting filter from the desired phase-response used in a subsequent allpass design. (Alternatively, the phase response of the loop filter can simply be neglected, as long as tuning is unaffected. If tuning is affected, the tuning allpass can be adjusted to compensate.)

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Dispersion Filter Design
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General Loop-Filter Design