Re: Upsampling and Interpolation for TDOA Correlation

Perhaps I didn't explain myself especially well. What I'm wondering is
according to sampling theorem shouldn't I be able to perfectly reconstruct
a signal sampled above its nyquist frequency (as the 128khz bandlimited
data is)? If I can reconstruct that, and the data arrived a few
nanoseconds later at one receiver than at another, shouldn't I--since I
can reconstruct the signal perfectly--be able to interpolate the data so
as to realize the couple-of-nanoseconds delay between the two arrivals?
If so then how? If not, then what's the flaw in my reasoning?

Thanks

DK


DonkeyKong skrev:
Hi y'all,

I'm working on developing a TDOA system with a desired time resolution
of
1ns (~1ft). However, the hardware I'm using restricts me to 1-2MSps
for
each signal being correlated. Typical correlation signals are in the
430MHz band and occupy a bandwidth in the ballpark of 128kHz. The
problem
I've encountered is that as much as I can simulate and successfully
correlate delayed signals if I construct them at 1GSps resolution in
Matlab, when I construct 1MSps signals and attempt to upsample and
interpolate before correlation, the signals fail to correlate to the
correct time difference. e.g. signals simulated at 1GSps and offset
by
5ns will have a correlation peak which corresponds to 5 samples, but
signals simulated at 1MSps and offset by 5ns, when upsampled and
interpolated to 1GSps, correlate to a peak, but that peak doesn't
correspond to 5 samples (5ns) of separation. Does the peak get moved
by
the process of upsampling/interpolation, and if so is it possible to
convert it back into a meaningful time delay?

You aim at an "effective" sampling rate of 1 GHz, but is restricted to
a
practical sampling rate of 1 MHz? To get past that, you try to
interpolate
the data you actually get.

I don't see any reason why this should work. The process of
"interpolation" only implies that you impose your own "prejudice"
on the data, you don't get anything new out of it that you did not
get from the original data.

This seems like a simple enough reconstruction problem since my
sampling
hardware isn't coherent with the data and so I should be able to
correlate
on the TDOA of the data (shouldn't I?), but once I interpolate this
just
isn't happening.

These are two different questions: estimate fractional-sample time
delays
from correlation or interpolate to find the fractional-sample time
delay.

There is one trick you could try, based on analyzing the phase of the
cross spectrum between your two signals. I did get a crude version
to work for fractional-sample time delays, but you are aiming for
1/1000th of a sample, so...

Rune




.

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