room impulse response and deconvolution

[Magnus Danielson]

From: Martin Czech <martin.czech at intermetall.de>
Subject: room impulse response and deconvolution
Date: Thu, 20 Jan 2000 19:43:20 +0100 (MET)

> Again room responses.
> 
> One of the problems is that I can not apply a unit impulse
> to the room. Balloons look more like differentiated unit pulses,
> and together with microphone far worse then that. So
> the recorded response is somehow convoluted with an unpleasant function.
> 
> One can try to deconvolute this, but the problem was, that:
> 
> 1. time domain deconvolution is impossible for fixed sequence length

Hmm... this does not correlate well with my understanding here... please
elaborate so that I can understand who of us got something wrong (possibly
both ;).

I assume that we are talking about stripping of the source impulse responce
from the sampled impulse responce. If this is what you mean I think that this
is fully possible in the time domain using cross-correlation. This is a simple
multiplication between the samples in a orderly fashion. It's simple math and
simple code but just expensive.

If you see that I am of track, please enligthen me on that.

I have been using cross-correlation techniques to measure impulse responces of
audio range. It is a well founded method and corrections can be applied.
This is also the method I proposed earlier in order to measure impulse
responces of rooms etc.

> 2. seems to not converge for infinite sequence length
> 3. frequency domain deconvolution operates circular, ie.
>    expects the deconvolution filter only to work with circular
>     convolution, which is not what we need.
>     
> After running arround in the woods for a couple of hours I thought
> that linear convolution yields the same result as circular, if
> only the deconvolution filter is repeated again and again,
> of course, because this will mimic circularity for a while.
> 
> Ok, experimental software rewritten, cat copies 3 times the 
> deconvolution filter sequence, convoluted with the balloon free
> air response, voila, two nice sharp unit pulses in the middle,
> and of course some trash at the beginning and the end.
> But a silver lining. As you might have guessed, the next step
> is proper windowing, as always if abrupt sequnence ends have to
> be fixed. 
> 
> First experiments with a simple trapezoid window give encouraging results,
> a sharp unit impulse of magnitude 4000, and some garbage arround,
> but smaller then 50. 
> 
> The next steps should improve the window, and also verify that the garbage
> can not be heard because of masking by the big unit pulse.
> 
> So things get better.
> 
> The poor man's method (balloon) seems still to be reasonable for 
> acoustic measurements. 

Here's a trick:

You could use the direct sound from the balloon (up to the first reflection)
and use that and cross-correlate that to the full sample and by that remove
the balloons impulse responce from the rest in order to acheive a better
resulting room responce. The Achilles heel of this method is that you basically
assume that the impulse responce of the balloon as it pops is idealy the same
in all directions (which is isn't). It may be so that it is equalent enougth
so that the improvement is better.

The same type of problem actually exist with every source. A balloon has
probably much tighter impulse responce diffrances than an ordinary speaker.

Could anyone send me a self-freefloating pulsating sphere I could use?

> And for electronic measurements (electronic reverbs) I could
> try repeated pulses (signal enlarges by N^2, but noise only by N),
> so S/N can be improved (and is critical if it is hissing broad band
> noise).

An interesting note here... an appropriate level of noise will help you get
over non-linearaties in A/Ds if you can do repeated measurements. Too low noise
level will let the non-lineareties come out, too high noise level will make
the noise come out (and thus require unecessary measurements to remove).

Cheers,
Magnus