On Mon, Nov 15, 2010 at 10:54 AM, Mathieu Bouchard <matju@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?