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I'm looking at Harmor specifically, but my question is about resynthesis in general. I assume that Fourier analysis is how these engines break a sound down into its constituent partials with frequency, amplitude, and phase information. But if that is the case, I am confused, because I thought there were some pretty significant trade-offs between frequency resolution and time resolution which were inherent in Fourier analysis (like not limitations in the implementations, but in the actual algorithm itself). E.g. when I narrow the sampling window in my spectrum analyzer (to get better temporal resolution), my frequency axis gets all "blured". When I widen the window, I get much better frequency resolution, but at the cost of temporal resolution.

How do resynthesis engines [seem to] get around this limitation? Or am I wrong about the limitations in Fourier Analysis? (or just wrong in thinking that these engines even use FA?)

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    It looks like SPEAR can do either FA-based resynthesis (probably more precisely IFFT or Inverse Fast Fourier Transform) or it can do "[noise modulated] oscillator bank synthesis with optional cubic phase interpolation as in the classical McAulay-Quatieri method" for resynthesis. So Hamor might have the same capabilities. See (quoted above): klingbeil.com/data/Klingbeil_Dissertation_web.pdf – Todd Wilcox Nov 19 '15 at 21:10
  • This is the first time I've seen resynthesis engines and they look very interesting. I know a bit about Fourier analysis and you are correct there is frequency/time tradeoff. However I imagine in this case it is not that significant. For example if we are sampling audio at 44.1kHz then it will only be on very small timescales that we don't have enough data points for an 'accurate' Fourier representation (of low frequencies). It is very unlikely therefore the the time frequency trade off matters. – rwolst Nov 24 '15 at 17:56
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    This question reminds me of Heisenberg's uncertainty principle. – Marc W Nov 28 '15 at 19:17
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I just had a look at Harmor and I'm assuming your question is "How can resynthesis engines be so accurate at RECONSTRUCTING SOUND despite the time/frequency resolution trade-offs inherent in Fourier analysis?"

Well put simply, the time frequency decomposition, be at a wavelet transformation or short time Fourier transform is just another representation of the sound. No information is lost in the process and one can transform between the two representations without any loss in accuracy.

What the time/frequency resolution tradeoff is saying is that if I only observe a small number of data points (in time), my transformation will be limited in the number of frequency components. This doesn't mean we will not be able to reconstruct the original signal (after all it did not consist of much information).

If however you put a short snippet of a sound into Harmor and you wished to play a longer sound using this snippet, your longer sound would not have any frequency components lower than those found in the original snippet. Therefore if you want to get an accurate resynthesis of a sound, make sure you put in a long enough sample. Note that if you're sample rate is 44.1kHz then any reasonable length sample should capture most of the important frequency information in the human hearing spectrum.

I would recommend reading the Wikipedia link on Fourier transforms

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