### EDR-Based Loop-Filter Design

This section discusses use of the Energy Decay Relief (EDR) (§3.2.2) to measure the decay times of the partial overtones in a recorded vibrating string.First we derive what to expect in the case of a simplified string model along the lines discussed in §6.7 above. Assume we have the synthesis model of Fig.6.12, where now the loss factor is replaced by the digital filter that we wish to design. Let denote the contents of the delay line as a vector at time , with denoting the initial contents of the delay line. For simplicity, we define the EDR based on a length DFT of the delay-line vector , and use a rectangular window with a ``hop size'' of samples,

*i.e.*,

^{7.13}

^{7.14}An online laboratory exercise covering the practical details of measuring overtone decay-times and designing a corresponding loop filter is given in [280].

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