Digital Waveform comparision question

when trying to determine the correlation between a waveform contained
in two asynchronously  sampled series, either through cross
correlation or other techniques, is it common to perform some type of
signal reconstruction beforehand?

It would seem if I am sampling at 4x the max bandwidth, the max
possible phase difference would yield huge errors if I just compared
sample to sample (take two 50Hz sine waves randomly sampled at 200Hz
for instance).

Now if I reconstructed the intermediate points with a sinc function,
obviously, I could obtain much better results, or alternatively
oversample by 10 or 20x.

steve

On 8 Apr, 00:39, "steve" <bungalow_st...@yahoo.com> wrote:
> when trying to determine the correlation between a waveform contained
> in two asynchronously  sampled series, either through cross
> correlation or other techniques, is it common to perform some type of
> signal reconstruction beforehand?

It depends on what you mean by "asynchronous sampling."
I would expect that two time series which are sampled
with the same samling rate ought to be comparable.
If there two sampling rates in the two systems are off
by a "significant" amount, things might become worse.

> It would seem if I am sampling at 4x the max bandwidth, the max
> possible phase difference would yield huge errors if I just compared
> sample to sample (take two 50Hz sine waves randomly sampled at 200Hz
> for instance).

"Randomly sampled" is an ambiguous term. Do you mean that
the dat are sampled at random points, or at a fixed samling
rate but with random phase?

> Now if I reconstructed the intermediate points with a sinc function,
> obviously, I could obtain much better results, or alternatively
> oversample by 10 or 20x.

Assuming you want to measure relative time delays, you
could consider analyzing the phase of the cross spectrum.

Rune

On Apr 7, 4:08 pm, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> On 8 Apr, 00:39, "steve" <bungalow_st...@yahoo.com> wrote:
>
> > when trying to determine the correlation between a waveform contained
> > in two asynchronously  sampled series, either through cross
> > correlation or other techniques, is it common to perform some type of
> > signal reconstruction beforehand?
>
> It depends on what you mean by "asynchronous sampling."
> I would expect that two time series which are sampled
> with the same samling rate ought to be comparable.
> If there two sampling rates in the two systems are off
> by a "significant" amount, things might become worse.
>
> > It would seem if I am sampling at 4x the max bandwidth, the max
> > possible phase difference would yield huge errors if I just compared
> > sample to sample (take two 50Hz sine waves randomly sampled at 200Hz
> > for instance).
>
> "Randomly sampled" is an ambiguous term. Do you mean that
> the dat are sampled at random points, or at a fixed samling
> rate but with random phase?
>
> > Now if I reconstructed the intermediate points with a sinc function,
> > obviously, I could obtain much better results, or alternatively
> > oversample by 10 or 20x.
>
> Assuming you want to measure relative time delays, you
> could consider analyzing the phase of the cross spectrum.
>
> Rune

I meant fixed sampling. I'm not interesed in relative delay, but a
measure of similarity of the two waveforms (as a simple example say a
pure sine wave as a template compared to an incoming distorted sine
wave)

On 8 Apr, 02:50, "steve" <bungalow_st...@yahoo.com> wrote:
> On Apr 7, 4:08 pm, "Rune Allnor" <all...@tele.ntnu.no> wrote:
>
>
>
>
>
> > On 8 Apr, 00:39, "steve" <bungalow_st...@yahoo.com> wrote:
>
> > > when trying to determine the correlation between a waveform contained
> > > in two asynchronously  sampled series, either through cross
> > > correlation or other techniques, is it common to perform some type of
> > > signal reconstruction beforehand?
>
> > It depends on what you mean by "asynchronous sampling."
> > I would expect that two time series which are sampled
> > with the same samling rate ought to be comparable.
> > If there two sampling rates in the two systems are off
> > by a "significant" amount, things might become worse.
>
> > > It would seem if I am sampling at 4x the max bandwidth, the max
> > > possible phase difference would yield huge errors if I just compared
> > > sample to sample (take two 50Hz sine waves randomly sampled at 200Hz
> > > for instance).
>
> > "Randomly sampled" is an ambiguous term. Do you mean that
> > the dat are sampled at random points, or at a fixed samling
> > rate but with random phase?
>
> > > Now if I reconstructed the intermediate points with a sinc function,
> > > obviously, I could obtain much better results, or alternatively
> > > oversample by 10 or 20x.
>
> > Assuming you want to measure relative time delays, you
> > could consider analyzing the phase of the cross spectrum.
>
> > Rune
>
> I meant fixed sampling. I'm not interesed in relative delay, but a
> measure of similarity of the two waveforms (as a simple example say a
> pure sine wave as a template compared to an incoming distorted sine
> wave

There is a standard text which deals with such questions:

Bendat & Piersol "Random Data" (Wiley 2000)

The key word to look for is "coherence".

Rune

On Apr 8, 6:15 am, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> On 8 Apr, 02:50, "steve" <bungalow_st...@yahoo.com> wrote:
>
>
>
>
>
> > On Apr 7, 4:08 pm, "Rune Allnor" <all...@tele.ntnu.no> wrote:
>
> > > On 8 Apr, 00:39, "steve" <bungalow_st...@yahoo.com> wrote:
>
> > > > when trying to determine the correlation between a waveform contained
> > > > in two asynchronously  sampled series, either through cross
> > > > correlation or other techniques, is it common to perform some type of
> > > > signal reconstruction beforehand?
>
> > > It depends on what you mean by "asynchronous sampling."
> > > I would expect that two time series which are sampled
> > > with the same samling rate ought to be comparable.
> > > If there two sampling rates in the two systems are off
> > > by a "significant" amount, things might become worse.
>
> > > > It would seem if I am sampling at 4x the max bandwidth, the max
> > > > possible phase difference would yield huge errors if I just compared
> > > > sample to sample (take two 50Hz sine waves randomly sampled at 200Hz
> > > > for instance).
>
> > > "Randomly sampled" is an ambiguous term. Do you mean that
> > > the dat are sampled at random points, or at a fixed samling
> > > rate but with random phase?
>
> > > > Now if I reconstructed the intermediate points with a sinc function,
> > > > obviously, I could obtain much better results, or alternatively
> > > > oversample by 10 or 20x.
>
> > > Assuming you want to measure relative time delays, you
> > > could consider analyzing the phase of the cross spectrum.
>
> > > Rune
>
> > I meant fixed sampling. I'm not interesed in relative delay, but a
> > measure of similarity of the two waveforms (as a simple example say a
> > pure sine wave as a template compared to an incoming distorted sine
> > wave
>
> There is a standard text which deals with such questions:
>
> Bendat & Piersol "Random Data" (Wiley 2000)
>
> The key word to look for is "coherence".
>
> Rune- Hide quoted text -
>
> - Show quoted text -

ok, I will check it out, thanks