Parameter smoothing for delay line? – Page 4 – DSP and Plugin Development Forum

Trying to explain the same a bit more visually… So suppose you are having an effect unit (a filter or a delay) with a single variable parameter (cutoff or delay time). If this parameter variation is representable as time warping, we could write the processing as

out = U( E( W(in) ) )

where E is the effect processor, W is the time-warper and U is the time-unwarper.
Or, graphically

in ——-> W ——-> E ——–> U ——-> out

Now W and U are memoryless processors, which also preserve the vertical aspects of the signal shape (such as the vertical range, number of oscillation cycles, etc.). They also preserve the signal’s smoothness to an extent to which the time-warping itself is smooth. So no drastic changes to the signal shape at all, only horizontal stretching/compression.

E is the only processor which has memory. But now it’s totally static, all modulation has been incorporated into W and U. That is, effectively we are having a fully static setup, except that we’re having some time-warping processors in it. In that sense, the processing of the signal by such setup is essentially static, the only dynamic parts being contributed by time-warpers, but those are just horizontal deformations of the signal.

This e.g. immediately explains why with the tape delay the feedback repetitions of one and the same delay period never overlap, but continue repeating in one and the same form. It’s because the setup is essentially static, the input signal just gets warped once by W, and then repeats inside a static delay E.