Hi
Specifically for the FFT: it would have to be a synthesis form tending
to have changes in many harmonics over the time of a IFFT interval,
where the harmonics are an integer of the base frequency. That's the
most logical answer, even though it only talks about the IFFT. Like some
here suggested you could do signal analysis with the forward FFT to
create "frequency samples", or real time effects, or parts thereof, but
that wasn't the question.
Probably it is also logical to look at applications of accelerated
computing for (I)FFTs, as it were to make use of the fastest (I)FFTs
around to make some form of synthesis with, which would make the(I)FFT
preferable over other frequency analysis/synthesis tools, which is
probably part of history.
In the context of synthesis, or intelligent multi sampling with
complicated signal issues, you could try to make the FFT analysis and
filtering a targeted part of the synthesis path, so that the playing
back of samples contain variations and sample information that can be
picked up and transformed by a FFT based signal path element. In some
form (not exactly as I described in general terms) I believe this is the
case with the Kurzweils.
Finally, you could build in pro-mixing "telephone line" sounds that a
complex mix setup can detect and make Equal Loudness Curve corrections
and even DAC (Signal Reconstruction) Transient Inter Modulation
corrections with.
Playing with the FFT in a sense common in sciences can be of use to all
kinds of approximations and components of a digital signal path
requiring fast frequency analysis, like speech coding in the 80s. I'm
sure I could come up with some interesting uses for my own string
simulator software, and a dozen other fun computations, with or without
good success, but I think work is more interesting where the analysis of
synthesis is done that prevents loudness wars and all kinds of ugly and
distorted signals. But that's hard, I've not seen many people work on that.
T.V.
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