comparing audio signals to determine delay

On Mar 20, 4:12 am, minfitl...@yahoo.co.uk wrote:
> On Mar 20, 9:52 am, "robert bristow-johnson"
>
> <r...@audioimagination.com> wrote:
> > On Mar 19, 4:32 pm, "naebad" <minnae...@yahoo.co.uk> wrote:
>
> > > Cross correlation does not work well when estimating delays (unless
> > > the signals are white). You need generalized cross correlation.
>
> > the signals need not be white, but what they need to be is broadbanded
> > and *not* periodic, and then cross correlation works okay.
...
> No,  they need to be white for a good estimate of delay. There is not
> space to discuss it all here. You need to look at Knapp and Carters
> paper.
>
> Knapp, G.C. Carter, The generalized correlation method for estimation
> of time delay, IEEE Trans. ASSP. 24 (4) (1976) 320-326. ...

i don't have access to that paper (actually, that might be the one and
only year i was an IEEE student member), but i have actually worked on
this directly in the past and you CAN, using cross-correlation, get a
very accurate and unambiguous measure of difference in arrival time
between two microphone recieving the same sonic signal as long as it
is not periodic (or quasi-periodic) and it is *sufficiently*
broadbanded.  it does not need to be broadbanded from DC all the way
to Nyquist.  and it need not be white.

FYI, the application was about that of a TV reporter speaking into a
microphone out in the field and some loud truck would drive by and
drown out the reporter for a couple of seconds.  so the idea was to
use another microphone placed a meter or two away from the reporter
(usually above his head out of view if you could) and use an NLMS to
try to define a hypothetical filter between the ambient mic and the
reporter mic.  but because the interference sound could arrive at
either of the mics first, we had to measure the difference in time of
arrival and "center" the LMS FIR filter around that time.  the LMS
filter seemed to work like shit (didn't converge fast enough) but the
measure of path length difference using cross-correlation worked very
well when the common sound was loud, noisy, and not a tone.  it
certainly was not white, but it was somewhat broadbanded, but i would
not say broadbanded up to Nyquist.  the top two octaves probably had
very little energy in them.

r b-j

> No,  they need to be white for a good estimate of delay. There is not
> space to discuss it all here. You need to look at Knapp and Carters
> paper.
>
> Knapp, G.C. Carter, The generalized correlation method for estimation
> of time delay, IEEE Trans. ASSP. 24 (4) (1976) 320-326. ...


I briefly looked at the paper and I did not see any mention or proof
of whiteness being a necassary condition to obtain a *good* unique
estimate of the delay. In fact, it seems that the paper even recomends
pre-filtering the signal at locations with high SNR, which would
reduce the whiteness of the signal even futher...

Offcourse, a high power white signal would be the optimal signal to
esimate the delay because every sample is independent of each other
and with unique values (ignoring quantitazation effects). But that
does not mean that other signals can uniquely determine the lag
between mics as well...

Here is the abstract of the paper for those who are interested:

***
Abstract
A maximum likelihood (ML) estimator is developed for determining time
delay between signals received at two spatially separated sensors in
the presence of uncorrelated noise. This ML estimator can be realized
as a pair of receiver prefilters followed by a cross correlator. The
time argument at which the correlator achieves a maximum is the delay
estimate. The ML estimator is compared with several other proposed
processors of similar form. Under certain conditions the ML estimator
is shown to be identical to one proposed by Hannan and Thomson [10]
and MacDonald and Schultheiss [21]. Qualitatively, the role of the
prefilters is to accentuate the signal passed to the correlator at
frequencies for which the signal-to-noise (S/N) ratio is highest and,
simultaneously, to suppress the noise power. The same type of
prefiltering is provided by the generalized Eckart filter, which
maximizes the S/N ratio of the correlator output. For low S/N ratio,
the ML estimator is shown to be equivalent to Eckart prefiltering.

"Ikaro" <ikarosilva@hotmail.com> schreef in bericht 
news:1174414659.158897.36820@l77g2000hsb.googlegroups.com...
>> No,  they need to be white for a good estimate of delay. There is not
>> space to discuss it all here. You need to look at Knapp and Carters
>> paper.
>>
>> Knapp, G.C. Carter, The generalized correlation method for estimation
>> of time delay, IEEE Trans. ASSP. 24 (4) (1976) 320-326. ...
>
>
> I briefly looked at the paper and I did not see any mention or proof
> of whiteness being a necassary condition to obtain a *good* unique
> estimate of the delay. In fact, it seems that the paper even recomends
> pre-filtering the signal at locations with high SNR, which would
> reduce the whiteness of the signal even futher...
>
> Offcourse, a high power white signal would be the optimal signal to
> esimate the delay because every sample is independent of each other
> and with unique values (ignoring quantitazation effects). But that
> does not mean that other signals can uniquely determine the lag
> between mics as well...
>
> Here is the abstract of the paper for those who are interested:
>
> ***
> Abstract
> <cut>
>

I've found the paper and will take a closer look at it myself pretty soon. 
Some googling for the cross-correlation did turn up some nice pieces of 
information, which indeed makes it look like a suitable way to do what it's 
gotta do.. Of course, the sound of the surrounding will probably be far from 
periodic, so that won't be a problem..

Haven't got any response back with any information about the actual nodes, 
the university teachers are sooo busy these days... ahum... cough...

Still, lots of thanks for all the advices, it already helped me greatly this 
far..