Thinking about it, I recall there was some from of transform used for frequency/time
analysis for instance for radar problems (maybe books from before WWII, or more recent
frequency/time analyzers) and without checking though it was in popular DSP speak
something like the Hilbert transform, but it seems that's just about the idea of
transforming repeating waveforms for the purpose of analyzing harmonics.
It's possible to make a decent short filter that convolutes with a random or prepared
digital signal such as to create an indication of frequency. From that creating out of
phase synthesized sine tones shouldn't be a problem either, though I think the accurate
phase responses required for the binorals of the human hearing a very subtle and the
inherent results coming from the quickly browsed limited Hilbert transform as the
projection onto sine and cosine components seem nothing particularly suited to any effect
I know of at the moment.
I repeat the main problem, unless you'd have prepared and limited the domain of input
signals available and make credible you can do more accurate matching that way, is that
unless you do significant upsampling or high frequency sampling, the signal, or it's
integral usable for convolution between the samples is only properly reconstructed by a
long sinc interpolator. Any other filter, by mathematical incongruence and therefor
strictly logically speaking incorrect, doesn't do a perfect job, no matter how long ou
search for alternatives.
The idea of estimating a single sine wave frequency, amplitude and phase with a short and
easy as possible filter appeals to me though. Either there's the possibility of tuning an
interval to the wavelength, or using some form of filter that outputs an estimate.
T.
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