[PD] HHT HilbertHuangTransform objects in Pd?

Charles Henry czhenry at gmail.com
Mon Nov 15 19:06:30 CET 2010


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