On Mon, Nov 15, 2010 at 10:54 AM, Mathieu Bouchard <ma...@artengine.ca>wrote:
> On Mon, 15 Nov 2010, Charles Henry wrote: > > However, there's an interesting and useful approximation given by the >> hilbert~.pd patch (provided in the extra directory perhaps?). It uses two >> all-pass biquad filters that are ~90 degrees out of phase with each other to >> approximate the hilbert transform. >> > > Unfortunately, there are two different things called Hilbert Transform, and > the one with the two biquads doesn't approximate Hilbert's decomposition, > they approximate the other thing called after Hilbert. > (is that right ?) > I don't know... The Hilbert transform on a function g(t) is this thing: Hg = 1/pi * integral( s=-inf, inf , 1/(t-s)*g(s) *ds) or in other words, convolution by 1/(pi*t) and there's a complex valued signal based on g(t) h(t) = g(t) + i*Hg(t) The Hilbert transform gives you just the imaginary part. The hilbert~.pd patch approximates this complex valued signal h(t). I know there's a reference to single-sideband modulation in the help patch if that's related--is h(t) called the analytic signal?
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