Loop Feedback Control

Observation

The shorter a loop the more quickly it fades out.

Explanation

The feedback control sets the amount by which the volume is reduced per loop repetition. Thus, a shorter loop's volume will decrease by the same amount within less time than a longer loop.

Example

Feedback is set to 50%.
Loop A duration 10 s, feedback will decrease by 50% per repetition, i.e. every 10 seconds.
Loop B duration 5 s, feedback will decrease by 50% per repetition, i.e. every 5 seconds.
After 10 seconds Loop A will have diminished to 50%, Loop B will have diminished to 50% * 50% -> 25%

(assuming the feedback was moved exponentially down from 100% to 50% during the first run of the loop)
(assuming the feedback was moved briskly down from 100% to 50% during the first run of the loop. Thanks to Andy Butler for this graphic and for making the point.)

Parameters

ParameterSymbolUnitRangeDomain
feedbackF% (percent)0-100integer
loop durationLDs (seconds)[0,...real
process durationPDs (seconds)[0,...real
repetitions (number of)R[0,...integer
volumeV??real
initial volumeV0??real

Formulas

FormulaDescription
(1)V = V0 * (F/100)RResulting volume V at the end of repetition R for a loop with a feedback setting of F
(2)R = PD / LDNumber of repetitions depending on process duration and loop duration

Examples

What volume factor x will a 10-second-loop have decreased to after 60 seconds with a feedback setting of 80% ?

What feedback setting F will lead to a decrease in Volume by 90% within 30 seconds for a 10 second loop?

How many repetions R does it take until a loop's volume will have decreased to 10% with a feedback setting of 90% ?

Remarks

Thanks

© Bernhard Wagner, 2006.