[music-dsp] Envelope Detection and Hilbert Transform

James Chandler Jr jchandjr at bellsouth.net
Fri Sep 24 11:39:05 EDT 2004

Thanks for the explanation, Angelo

Here is a dummie followup question--

Your explanation well-explains the Hilbert advantage for finding the exact time 
of an envelope peak. However, if writing a dynamics plugin, a common aspiration 
is to minimize the envelope ripple (for any given release time constant).

Envelope ripple in a dynamics plugin causes intermodulation distortion. One 
might adopt a holy grail quest to write a compressor which responds very quickly 
to amplitude, but also has very low intermodulation distortion.

Many music tracks do not have well-behaved low-crest-factor signals.

Perhaps a good 'nightmare' envelope test signal, would be a triangle-modulated 1 
percent duty-cycle pulse wave.

I understand how a Hilbert envelope detector would help avoid ripple on 'well 
behaved' signals. But if the object is to minimize envelope ripple regardless of 
wave shape, would a Hilbert envelope detector be smart enough to smooth out 
'nightmare signals'? Perhaps one would also require post-Hilbert lowpass 
filtering? Dunno.

Admittedly this is a rather vague question, but if you have any thoughts on the 
issue, it will be appreciated.



----- Original Message ----- 
From: "Angelo Farina" <farina at pcfarina.eng.unipr.it>
To: "'Citizen Chunk'" <citizenchunk at gmail.com>; "'a list for musical digital 
signal processing'" <music-dsp at ceait.calarts.edu>
Sent: Friday, September 24, 2004 5:33 AM
Subject: RE: [music-dsp] Envelope Detection and Hilbert Transform

>> -----Original Message-----
>> From: music-dsp-bounces at ceait.calarts.edu
>> [mailto:music-dsp-bounces at ceait.calarts.edu] On Behalf Of
>> Citizen Chunk
>> Sent: 23 September 2004 22:57
>> To: a list for musical digital signal processing
>> Subject: Re: [music-dsp] Envelope Detection and Hilbert Transform
>> call me Mr. Stupid, but ... why is the Hilbert so accurate at
>> finding the peak amplitude? why not just rectify? hmmm ... TO
> The explanation is simple. Let's take a sinusoidal signal, say at 440 Hz.
> Then we apply an amplitude modulation with a triangular shape.
> The "maximum" amplitude should occur at the vertex of the triangle.
> But if, by chance, this corresponds exactly with a zero-crossing of the sine
> wave, You will not get the maximum sample at that exact position! Instead,
> you will get two quasi-maximum values in correspondence of the two local
> maxima of the sine wave just before and above the theoretical true maximum
> point. The Hilbert transform reconstruct correctly the shape of the
> trinagular modulation, and provides You an accurate estimate both of the
> maximum amplitude of it and of its exact time position.
> Bye!
> Angelo Farina
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