[music-dsp] modelling a spring reverb

[Sampo Syreeni]

On 2002-09-23, James Chandler Jr. uttered to music-dsp at shoko.calarts.edu:

>Thanks Vesa. Will try FDN's next time I get a chance to experiment.

BTW, I just reread my second long post, and noticed that I forgot a
significant part of what real FDN's are like. At the time, I was thinking
about building the general concept in two parts, but somehow the beginning
and the end of the tale bifurcated into one. What came out was the
simplest of nasty simplifications one can do to a real FDN, not the (much
more useful) general case.

What I said was that FDN's are basically IIR versions of tapped delay
lines. However, this is only true in a very special case. The general case
actually keeps the delay lines separate, and performs a full NxN matrix
multiply to get the feedback -- N is the number of delay lines, and the
matrix multiply maps the output (column) vector into the input one. One
can inject the input signal into a single delay, into a single output or
scalar multiply it by a vector, adding the vector components in to the
delay inputs. The case I described is the extreme special case of all the
rows in the matrix being equal -- then one multiply per delay line
suffices, and the lines can be collapsed into a single tapped delay. In
the general case, this certainly does not hold -- typically, we'd like to
use a (scaled) orthogonal matrix so that energy isn't lost (is lost
exponentially) on the way from output to input.
-- 
Sampo Syreeni, aka decoy - mailto:decoy at iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2


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