Correlation Threshold Meaningful Value

Started by November 24, 2005
```Hi,

The autocorrelation of a signal X is generally bell-shaped with maximum
value at the middle. I am just wondering, from what a threshold value we
can assume practically that the signal autocorrelation is null?

Assume that the maximum value of the autocorrelation is M. if the
threshold cited above is equal to Per*M (where Per stands for percentage
or ratio), then by identifying the x label at Per*M autocorrelation value
a user can identify to what temporal shift, the signal samples can still
be correlated

Many thanks

```
```newsnetstudent wrote:
> Hi,
>
> The autocorrelation of a signal X is generally bell-shaped with maximum
> value at the middle. I am just wondering, from what a threshold value we
> can assume practically that the signal autocorrelation is null?
>
> Assume that the maximum value of the autocorrelation is M. if the
> threshold cited above is equal to Per*M (where Per stands for percentage
> or ratio), then by identifying the x label at Per*M autocorrelation value
> a user can identify to what temporal shift, the signal samples can still
> be correlated

The shape of the autocorrelation vs. delay depends on the nature if the
signal. It is cyclic with pure sinusoids and a spike with random (or
long pseudorandom) sequences.

Jerry
--
Engineering is the art of making what you want from things you can get.
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```
```Jerry Avins wrote:

> newsnetstudent wrote:
>
>> Hi,
>>
>> The autocorrelation of a signal X is generally bell-shaped with maximum
>> value at the middle. I am just wondering, from what a threshold value we
>> can assume practically that the signal autocorrelation is null?
>>
>> Assume that the maximum value of the autocorrelation is M. if the
>> threshold cited above is equal to Per*M (where Per stands for percentage
>> or ratio), then by identifying the x label at Per*M autocorrelation value
>> a user can identify to what temporal shift, the signal samples can still
>> be correlated
>
>
> The shape of the autocorrelation vs. delay depends on the nature if the
> signal. It is cyclic with pure sinusoids and a spike with random (or
> long pseudorandom) sequences.
>
> Jerry

And it is "practically" null when it has less energy than your
particular problem is sensitive to -- if you're trying to do
communications this may be 10% of full value; if you're doing
exceedingly sensitive measurements this may not occur until you're below
1 PPM.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
```
```newsnetstudent wrote:
> Hi,
>
> The autocorrelation of a signal X is generally bell-shaped with maximum
> value at the middle. I am just wondering, from what a threshold value we
> can assume practically that the signal autocorrelation is null?
>
> Assume that the maximum value of the autocorrelation is M. if the
> threshold cited above is equal to Per*M (where Per stands for percentage
> or ratio), then by identifying the x label at Per*M autocorrelation value
> a user can identify to what temporal shift, the signal samples can still
> be correlated
>
> Many thanks

In most practical situations the measured data will be contaminated
by noise, which is more or less correlated with the signal. I know,
all texts on statistical signal processing tell you that the
contribution
from the noise is a delta function, but that's the "true"
autocorrelation
sequence developed under quite strict theoretical conditions. In
practice
there will be a noise floor when you deal with measured data.

Now, under these *practical* conditions I would try to find an estimate

for the noise floor in the correlation sequence, and relate the
threshold
to that. Note that it might not be easy (or possible) to inspect the
autocorrelation sequence to find that noise floor. Even if you find it,

it needs not be easy to set a useful threshold.

So you basically have to evalueat each situation/data set to
determine how to set the correlation threshold. I know, it sounds
a bit defaitistic, but these types of *subjective* evaluations
occur all the time during data interpretation.

That's why it is called data *interpretation*.

Rune

```