Re: running Person's correlation

[Francesco Potortì]

>> I have a signal (long) and a template (short, fixed).  I have to compute
>> the Pearson's correlation of the short signal with a sliding window of
>> the long signal.  This is a convolution where each sample is divided by
>> the (fixed) standard deviation of the short signal and the running
>> standard deviation of the long signal.
>> 
>> The only loopless way I can think of is to compute a running sum, a
>> running sum of squares, and use them to compute a running standard
>> deviation to be multiplied with the convolution.  Any more
>> straightforward methods?

>filter() is the function you need to vectorize your code. However, the
>big question is whether you need a causal algorithms (i.e. only samples
>from the past can be used), or whether you can use a symetric sliding
>window. 

It should be causal, because after testing it has to be implemented on a
real-time system.
However, I do not mind about delays, so this should not be an issue.

>        It will make a big difference how to estimate the running mean
>and standard deviation. Below, there is an outline of the code you are
>looking for, the code snippets are not tested

Thank you for the code.  However, I do not want a long-term standard
deviation estimate.  What I want is a running Pearson's correlation, so
the standard deviation has to be a running one, that is, computed over
the correlation window.

What I am looking for is not linear with respect to its input, so using
filter() is not enough.  What I am doing now is to compute the
convolution (this can be done with filter) and then divide by a
running standard deviation computed using sum and sumsq.

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