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convolution reverb is a well known thing to us all... however, what about convolution compression? can it work? what do you think?

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I am not sure how to wrap my head around this concept of convolution compression. Are there impulse responses involved? Whereas convolution reverb is an attempt to create or simulate a space, convolution compression is what exactly? –  Hubert Campbell Jul 1 '10 at 16:59
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The convolution part of Convolution reverb refers to the math involved in generating the space as given by the Impulse response. I don't see where the complicated math would figure in compression. A sound hits a threshold, the compressor reduces the volume based on the ratio set by the user for a set amount of time also set by the user. Where does convolving factor in? –  Hubert Campbell Jul 1 '10 at 22:35
    
@Hubert I think he's talking about sampling a compressor to use it as a plug-in? Kind of like sampling an LA2A to make it a plug-in... Right? –  Utopia Sep 21 '11 at 22:40
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7 Answers

up vote 2 down vote accepted

As far as i understand it, an impulse response can be created of any piece of equipment. Modeling equipment and modeling a space are both based on the same principles.

I think the best way of understanding/explaining this is probably to look at how we can model an EQ.

An analog EQ can be modeled in the digital world through two main ways, first by either looking at a frequency domain response or a time domain response. Every frequency response has an equivalent time domain (impulse) response because the two are inextricably linked. Using the process of Fourier Transformation we can turn a time domain (impulse) response into an equivalent frequency domain response.

If you change the way a filter responds in frequency you also change how it responds in time, and vice-versa.

Therefore theoretically it is possible to model the characteristics of a given EQ by simply measuring its impulse response and modeling it in the digital world (the same as we make an impulse response of a space). The way in which this impulse response is applied to a digital signal is through the process of Convolution.

The way in which this is implemented is where it becomes a bit more tricky.

A single sample from a stream of samples from the input signal 'triggers off' the impulse response which is then scaled by the amplitude and phase value of the input sample, a sample later the same then happens to the second sample. The second sample is then added to the first, the third sample undergoes the same treatment but again a sample later, this then goes on and on for each successive sample in the input signal.

Essentially Output = Input*IR (here * means convolution)

But convolution is not just a simple process of multiplication, but the resulting sum of many many multiplications.

For example if we have an input signal that is 3 samples long (just for simplicity) with amplitudes at 11, 4 and 2. And a IR of 5 samples with amplitudes at 0.3, 0.6, 0.9, -0.4 and -0.2, we end up with 7 samples (remember because the samples are processed successively by one sample). This then give us the following multiplications and summations:

Sample 1 = (11x0.3) = 3.3

Sample 2 = (11x0.6)+(4x0.3)+0 = 10.63

Sample 3 = (11x0.9)+(4x0.6)+(2x0.3) = 12.9

Sample 4 = (11x -0.4)+(4x0.9)+(2x0.6) = 0.4

Sample 5 = (11x -0.2)+(4x -0.4)+(2x0.9) = -2

Sample 6 = 0 + (4x -0.2) + (2x -0.4) = -1.6

Sample 7 = 0+ 0+ (2x -0.2) = -0.4

(Sorry if thats a bit confusing, its a bit easier to see/understand if you plug it into excel and make some graphs)

Obviously these are just arbitrary numbers and really small sample numbers, even at 44.1kHz we end up with 100,000s of sample points for an impulse response. This, and the amount of variables in control positions for a device, means that creating a usable compressor based on IRs and convolution is very complex (hence the 'unique patented Dynamic Convolution process' of the Liquid mix im guessing). So yes, in a very long about way, convolution compression can work. Im not sure but i think the UAD plugs also work on a variation of these ideas, and there are probably many more. I think like any new digital technology it will probably a while for it to be perfected though.

EDIT:

yeah, endolith is right about Linear and Time-Invariant stuff. I'm thinking that the "dynamic convolution" they talk about in the things like the Liquid Mix is probably used in some way for capturing the "tone" of the compressor, and used in combination with other techniques to model a compressor. I'm far from an expert though, and I might be way off...

I've also found a couple of links that are pretty interesting reading: http://www.sintefex.com/docs/appnotes/compsim.pdf http://www.uaudio.com/webzine/2004/july/index2.html

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You know what... I think I just need to see it in action. Is the objective here to emulate other compressors? What would I hear from a Convolution Compressor that I could not appreciate from your average compressor that's popular on the market now? –  Hubert Campbell Jul 3 '10 at 0:13
    
"As far as i understand it, an impulse response can be created of any piece of equipment." Sure, but a single impulse response doesn't characterize the equipment unless the equipment is linear and time-invariant. An EQ (or any other filter) is an LTI system, and so a single impulse response is sufficient. If the response changes for different amplitudes (the very definition of a compressor), then you can't model the system with a single impulse response, and therefore can't model the response of the system using a convolution. –  endolith Jul 8 '10 at 2:58
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@Josh you bad man! –  Fred Pearson Sep 21 '11 at 16:43
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@Josh - my head just exploded. –  Jay Jennings Sep 23 '11 at 7:54
    
@Jay Sorry! haha, I think I might have drank too much coffee... –  deleted Sep 24 '11 at 14:20
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From what I've read -- days ago, when I was creating my first impulse responses -- you can't technically get a compressor IR to work. Sure, you can get it's coloring, but it will never actually compress -- that's just the science of convolution.

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Focusrite Liquid Mix/Channel do work with IR's for there compression. You only need a lot if IR's in order for it to work (compression is non-linear and IR's are so you need a lot of them to cover all gain levels). This is of course very CPU intensive and that is why it is not mainstream yet. But in the near future you will see this technique grow into the plugin world fast.

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You do get a working compressor from an impulse-set, but it's FAR from the real McCoy I'm afraid. To actually get a faithful reproduction of a compressor you need to see exactly what settings it has that will color the sound, and then sample it in all possible configurations.

Ofcourse, I doubt most IR-compressors are actually very comprehensive, and the ones I've tried was rather boring, but if there are a specific sound you want & don't really care for a more personal touch or effing wildly with the settings (which is something at least I finds extremely creative occasionally), then it´s an easy and cheap way to go.

Many earlier compressors didn't have any other settings than input and output, in these cases it's much easier. But still needs a good set of different levels for the output-IR's.

I love my convolution reverbs a lot, but when it comes to compressors and filters, I will continue using plugins and hardware. Much of my personal style as a designer comes from finding the personality and strengths of my (mostly) outboard equipment, both things normally considered good as well as flaws, I can use as tools in my creativity. To capture these things you must know full well what you want before you do the capture, and that pretty much kills the whole idea of exploiting the stuff as hard as possible to begin with...

Haven't used any in a long time though, so chances are they might have grown better with calculating the middle settings, but I still prefer hardware, I use imperfection in my search for perfection.

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Have you heard of the Nebula vst plugin (http://www.acustica-audio.com/)? It features something akin to dynamic IRs called "Vectorial Volterra Kernels". The net effect is that it can model non-linear effects and signal paths. I've tried it out; some aspects are amazing, some are not quite what you hope. But it's certainly worth a try... plus there's a free version.

Compressors do indeed work, but sound best at subtle settings. Also, there are some amazing 3rd party models of different console signal paths that work quite well.

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Nebula sounds fantastic, it's just a bit of a faff and a drain on system resources! –  Nicklaus Sep 23 '11 at 11:31
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Are you talking about modeling a real device by getting an impulse response from it and then convolving the impulse response with the signal to simulate the compressor? Using convolution that way only works for linear time-invariant systems, and compression is non-linear, so that wouldn't work.

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@endolith is right about LTI systems and convolution. Nevertheless you can try to build an environment, that will capture certain aspects of a compressor in numerous IRs, as others pointed out below. So you would build a framework to compensate for the lack of convolution to work on non-linear systems, but the IRs (alone) will not reproduce all the characteristics of the compressor, as they do for example with reverb. Another neglected fact is that IRs from parametric reverb gear often only capture one state as those machines use modulation to give the rooms more variation. –  user891 Sep 21 '11 at 17:31
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The only times I've seen "convolution" used in reference to compresson or any other dynamic processes is with products that model vintage compression units or mic pres. Take Liquid Mix, for example. It claims "the unique patented Dynamic Convolution process delivers unparalleled EQ and Compression emulations." Sounds a bit like they're using convolution as a buzzword.

Modeling equipment is one thing, getting the IR of a space is another. I'm not sure how one that creates echoes and adds and subtracts from the EQ could be applied to something that is essentially gain control. Perhaps you could use an IR to selectively compress certain frequencies.

Do you have something specific you're refering to?

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