posted 12 February 2002 16:22            

At least that is the theory. I suspect the practice is considerably more difficult.

posted 13 February 2002 13:31            

We humans, on the other hand, do it in our minds all the time, without realy thinking about it. So it ought to be posiable, but I don't know of any computer or equipment that even comes close to doing it. (YET!!)

Here is a posiable starting point.

If we start with a signal and put it through a single delay (no feedback) with its output amplitude reduced slightly and then mixed it in with the original signal. We can then put that mix into another delay with identical time settings and set the feedback to the output amplitude of the first delay, multiplied by minus one. This will give us the original signal with no delay.

posted 14 February 2002 06:14            

Pete has a pretty neat idea there, but there is one BIG problem with attempting deconvolution... Namely, some frequencies get eroded so badly in the original convolution process that you can never get them back. If you try just straightforward deconvolution by dividing transfer functions you find that the divisor has some frequencies where it is nearly zero, and so the result is a massive amplification of noise at those frequencies.

When you know the nature of the noise field in your recordings, then very best you can do is a technique called Wiener filtering. Trouble is, you don't always know the noise field all that well. But this is the technique used by all those noise removal programs that make you startup in a dead spot so it can calibrate the noise field for removal. But noise removal, like deconvolution, always throws some of the valid signal away with the undesirable portions and the result is probably going to be slightly disappointing in terms of audio quality.

Just the same, those noise removal programs often work wonders, and so maybe a Wiener filtering on your reverb recordings would work well enough too. I am very interested in this topic, as it has applications in many far reaching fields, not the least of which is audio processing.

For echos and some kinds of reverbs you can also try something called Cepstral analysis (that's an intentional twisting of the word "Spectral"). But this is tricky too, because it requires phase unwrapping in order to pull it off correctly, and if you have ever tried unwrapping phase you know how treacherous that can be...

...seems like I provided a sound that does Wiener filtering on self adjusting noise estimates. I wonder how that would work on your examples? But Kyma has a limitation of 1024 FFT cells per FFT. Getting longer deconvolutions requires some additional work like another one of my submissions for doing 4 times overlap add processing. But this begins to eat up DSP's in a real hurry. I wonder if the Lake box can do this sort of thing. I know they handle long convolutions -- that's their main talent. I don't know if they handle deconvolution... I rather doubt it...

Cheers,

posted 15 February 2002 08:12            

CONUNDRUM.kym

I'm not so sure

Attached is a sound "KYMA CONUNDRUM". It starts with a square/pulse wave and the goes through a single delay which is mixed in antiphase at unity gain. This forms a comb filter with a notch at the exact frequency of the square wave and at every harmonic. It has erroded the signal to absolute silence. If you open up the sound you can run it at the midway module and you will here the silence(or rather you won't here signal).
Then by putting it though the delay remover bit as I described before, you get the original signal back. YES from nothing !!!

MAGIC ??

not realy and I'm sure you'll work it out, but it is still an interesting phenomenon.

posted 15 February 2002 16:11            

I'll look closely at your Sound. I just downloaded it... but I suspect you are adding a bit of the original signal back in. You can't get something from nothing... But if you have found such a technique then you stand to get the Nobel Prize in addition to the numerous awards you have accumulated for your Master SoundCrafting!!

Cheers,

posted 22 February 2002 13:00            

I finally sat down and took a good look at your Conundrum sound...

The reason this works is the same reason that I puzzled over a while back with the Kyma "PsuedoIntegrator" Sound prototype. The idea behind the stock PseudoIntegrator is that one first PseudoDifferentiates the sound -- removing DC right? -- and then integrates that back to have everything but DC right? Wrong!

It turns out that the combination of PseudoDifferentiator followed immediately by the integrator block is absolutely a no-op, except for 2 samples of delay. That puzzled me for a while, and then I thought someone at SSC was just pulling our collective legs... And then I figured out why it behaves the way it does.

Your Conundrum sound is the same as the PseudoIntegrator prototype, but with a delay value of 20 samples. (BTW, if you just set everything in the delays and square wave source to 20 samp then you avoid the problem of requiring 44.1 KHz sample rates)

The reason the Conundrum and the PseudoIntegrator prototype behave the way they do has to do with the starting transient behavior of these blocks. The differentiator, or your first delay, let the first few samples through the system untouched. Then when these raw samples hit the integrator stage (your second delay) they serve as initial values for reconstituting the original sample stream.

In order to prevent this reconstitution, you would have to delay the startup of the integrator stage by several, in your case 20, samples. Only then would the integrator start with nothing and perform its job of reconstitution without the "DC bias". Or in your case, reconstitution of the signal would produce nothing, since the signal had been truly removed by your input stage and delay.

It was only after sitting down and really thinking about the startup transient behavior that I "got it". I almost got on the Forum here and wrote a question to SSC about their PseudoIntegrator and why they would put it in... Then I realized that their input stage was intended solely as an example to be replaced by your own sources. So in effect, they were sort of pulling our legs, but at the same time they provided a useful stage in the form of a delay with unity feedback and unity input gain. That really does have useful behavior.

So to wrap it all up, you have captured the first few samples (20 in this case) within the integrator and it is forever recirculating due to the unity feedback, and no subsequent input samples.

But maybe you already knew this, and YOU were pulling our collective legs?

- DM

[BTW... this conundrum holds for any signal whose period is a submultiple of your 20 samples. Try it with an oscillator whose frequency is set to 20 samp inverse and see...]

posted 22 February 2002 15:38            

I knew you'd get it . When I first worked on it I laid awake for two nights thinking about how it could be, before I realized that the first and last cycle doesn't get filtered out. I first played the trick on myself.

BTW it also confirms what you said earlyier about tape hiss or any imperfections in anti convolution. If we added any tiny signal at the silence point in the kyma sound, we would get an acumilative explosion of noise at the output, due to the unit feedback. This is after all a convelution and anti convelution of an over simplyfied impules responce , just one spike at twenty samples in.

So that Nobel prize has slipped out of my grasp once again. I must try harder.