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Force-Pulse Filter Design

In the commuted piano synthesis technique, it is necessary to fit a filter impulse response to the desired hammer-string force-pulse shape for each key and for each key velocity $ v_c$, as indicated in Figures 9.32 and 9.33. Such a desired curve can be found in the musical acoustics literature [488] or it can be easily generated from a good piano-hammer model (§9.3.2) striking the chosen piano string model.

For psychoacoustic reasons, it is preferable to optimize the force-pulse filter-coefficients in the frequency domain §8.6.2. Some additional suggestions are given in [467,519].
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