<br><br><div class="gmail_quote">On Mon, Nov 15, 2010 at 10:54 AM, Mathieu Bouchard <span dir="ltr"><<a href="mailto:matju@artengine.ca">matju@artengine.ca</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
<div class="im">On Mon, 15 Nov 2010, Charles Henry wrote:<br>
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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.<br>
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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.<br>
(is that right ?)<br></blockquote><div><br>I don't know... The Hilbert transform on a function g(t) is this thing:<br>Hg = 1/pi * integral( s=-inf, inf , 1/(t-s)*g(s) *ds)<br>or in other words, convolution by 1/(pi*t)<br>
<br>and there's a complex valued signal based on g(t)<br>h(t) = g(t) + i*Hg(t)<br><br>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?<br>
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