### Length FIR Loop Filter Controlled by Brightness'' and Sustain''

Another convenient parametrization of the second-order symmetric FIR case is when the dc normalization is relaxed so that two degrees of freedom are retained. It is then convenient to control them as brightness and sustain according to the formulas

 (10.1) (10.2) (10.3)

where is the period in seconds (total loop delay), is the desired sustain time in seconds, and is the brightness parameter in the interval . The sustain parameter is defined here as the time to decay by dB (or time-constants) when brightness is maximum () in which case the loop gain is at all frequencies, or . As the brightness is lowered, the dc gain remains fixed at while higher frequencies decay faster. At the minimum brightness, the gain at half the sampling rate reaches zero, and the loop-filter amplitude-response assumes the form

A Faust function implementing this FIR filter as the damping filter in the Extended Karplus Strong (EKS) algorithm is described in [454].

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