Paul Stoffregen wrote:
Does anyone have any suggestions or references for an efficient algorithm to
find the peak
of a bandwidth limited signal?
Hi,
I think without getting lost in quadratic algebra or endless searches for a holy grail
that doesn't exist that I don't take part in, you've answered the main theoretical
question yourself: to know the signal between the samples, you need perfect reconstruction
to the actual signal, and then analyze that.
Of course, like the "Fast Lookahead Limiter" from Ladspa or LV2 which I use regularly
does, you could up-sample to a reasonably high sampling frequency with the best tools
you've got, and hope the best of a tool that up-samples another 8 times (IIRC) and leave
it at it that if you're using decent input signals to your sampling path that there aren't
a great many signals actually mirrors around the Nyquist frequency so that a tool like
that will doe a reasonable flattening job.
Of course it's possible there's one peak in your signal at 1/4*PI between two samples such
that no matter what a rational fraction between samples you compute you could never find
it with infinite accuracy... I suppose however in most practical cases you can have a
pre-conditioned situation where you know which possible up-samplers are going to be used
on your decent digital signal product, like wide window sinc, standard short interpolation
and a couple of other methods (FIR/IIR approximations, wave shape approximations,
multi-band approaches, and for the pro's: average based frequency components with
multi-limited computations in the 96kHz or higher sampling domain). If you know what the
customers are going to use as up-sampler, and once with the final product you make a
reasonable quality wide-window sync up-sampled test run to see if there are any special
cases to tend to, you could work with that, unless people enjoy endless (but not
particularly useful) discussions on heuristics.
Theo V.
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