[sdiy] what is the amplitude envelope of a signal

[Grant Richter]

Since this started as talking DSP...

Isn't the amplitude envelope the sum of all the harmonic (or inharmonic)
envelopes? That is, take an DFT, then sum the amplitudes in all the
frequency bins and divide by the number of frequency bins?

You would have to use a small number of frequency bins to get fast response.

BTW, I saw a PBS program that said Aristotle invented the theory of limits
in 300 B.C., since that forms the basis for the Calculus and was not
rediscovered until the 1700's, it looks like mathematics is about 2000 years
behind original schedule ;^)

> From: "Czech Martin" <Martin.Czech at micronas.com>
> Date: Wed, 1 Oct 2003 12:54:57 +0200
> To: "Harry Bissell Jr" <harrybissell at prodigy.net>, "Synth-DIY list"
> <synth-diy at dropmix.xs4all.nl>
> Subject: RE: [sdiy] what is the amplitude envelope of a signal
> 
> Harry,
> 
> your reply shows that you listened carefully to your
> results. These are exactly the problems I came across.
> 
> For such applications the usual circuits/ideas do not perform
> too well, or they are even useless.
> 
> Your "eye" approach is into the same direction of what
> I tryed, unfortunately this is a very intelligent
> approach. For the human beeing it is not too hard
> to draw the envelope, but automatons have problems...
> 
> m.c.
> 
>> -----Original Message-----
>> From: owner-synth-diy at dropmix.xs4all.nl
>> [mailto:owner-synth-diy at dropmix.xs4all.nl]On Behalf Of Harry
>> Bissell Jr
>> Sent: Mittwoch, 1. Oktober 2003 01:29
>> To: Richard Wentk; Synth-DIY list
>> Subject: RE: [sdiy] what is the amplitude envelope of a signal
>> 
>> 
>> OK then... lets make a formal definition  ;^P
>> 
>> The "envelope" of a signal is what your 'eye'
>> would process looking at the rectified or absolute
>> value of a signal.
>> 
>> The envelope would be a 'best fit' curve to that.
>> 
>> Single constant generators do not work (for me)
>> I'm processing a guitar, which has the following
>> nasty habits
>> 
>> 1) The positive and negative half cycles do not
>> have equal amplitude... and this change is variable
>> over time. Usually there is one large peak of one
>> polarity, followed by two smaller peaks of the
>> opposite
>> polarity.
>> 
>> 2) The guitar has a normal exponential decay, but the
>> decay time can be changed easily (on the fly) by
>> adding
>> damping to the strings in small or even large amounts.
>> The biggest problem is that if you mute the strings...
>> it will take forever for a single constant to get to
>> the
>> correct value.  The next note will start at the wrong
>> value... maybe a too high value if the next note is
>> more quiet.
>> 
>> The ripple vs speed tradeoff is a killer.  Any ripple
>> (which the 'best fit' or 'eyeball' curve conveniently
>> filters out) will cause noticible intermodulation
>> distortion especially if you are using the CV to drive
>> a filter.  Any lag will destroy the accuracy of the
>> original waveform.  Now maybe your guitar, or drum
>> has a real noticible attack time.
>> 
>> This is a real nightmare problem.  If I could stand
>> it, 
>> I'd think about running some delay in the signal to
>> allow the circuit to 'look into the future' and
>> adapt... but I fear even a millisecond is too much
>> 
>> H^) harry
>> 
>> 
>> --- Richard Wentk <richard at skydancer.com> wrote:
>>> At 13:08 30/09/2003 +0200, Czech Martin wrote:
>>>>> If you're getting signal breakthrough it means
>>> either there's
>>>>> some signal
>>>>> breakthrough in the circuit due to a design or
>>> construction
>>>>> fault, or the
>>>>> filtering isn't working properly, or both. The
>>> output should
>>>>> be a slow *DC*
>>>>> variation. There should be no effective signal
>>> content above
>>>>> 100Hz at the
>>>>> very maximum, and 10Hz would be more typical for
>>> many applications.
>>>> 
>>>> That is a good question. A lowpass with 100Hz or
>>> even 10Hz
>>>> gives problems with signals that have a short
>>> attack.
>>> 
>>> But are those problems severe enough to make a
>>> musical difference? I can't
>>> think of many applications where a dual
>>> time-constant standard follower
>>> circuit wouldn't produce useful results. And people
>>> have been using single
>>> constant followers since Bob Moog's days without
>>> worrying too much about it.
>>> 
>>>>> The only way to create a perfect envelope
>>> follower is to do
>>>>> it digitally in
>>>>> non-real time, where you can go forward and
>>> backtrack with an
>>>>> adaptive
>>>>> time-constant and some clever logic.
>>>> 
>>>> This is what I tryed, now I found that I can not
>>> write down
>>>> a formal description of "envelope", because I do
>>> not know
>>>> what it really is.
>>>> 
>>>> Like I said, I thought I knew exactly what it is
>>> about, but
>>>> when it comes to a formal description (algorithm) I
>>> know
>>>> nothing about.
>>> 
>>> That's because it's an ad hoc thing that doesn't
>>> have a formal definition.
>>> However you do it you'll always have a trade-off
>>> between responsiveness and
>>> accuracy, especially on transients.
>>> 
>>> If you want a digital interpretation, pick your time
>>> constant, sample
>>> sections equivalent to its duration, calculate the
>>> RMS value in each (not
>>> too hard digitally) and then interpolate the values
>>> to create a curve. Use
>>> cubic instead of linear interpolation for a smoother
>>> result.
>>> 
>>> For adaptive tracking lower the time constant by a
>>> few factors whenever you
>>> see a transient (i.e. a very rapid change in RMS
>>> level), shift the start of
>>> each RMS window to the beginning of the transient,
>>> and then increase the
>>> time constant again during the release or decay
>>> period. This won't track
>>> reverse transients but it will handle most other
>>> things.
>>> 
>>> You can include a reverse transient check if you
>>> want to get really picky.
>>> 
>>> This solution won't work in real time because
>>> there's some lookahead and
>>> lookback is involved, but it will give you the best
>>> possible results
>>> otherwise.
>>> 
>>> Richard
>>> 
>>> 
>> 
>> 
> 
>