[Numpy-discussion] Definition of correlation, correlate and so on ?

[David Cournapeau]

Hi,

    I am polishing some code to compute autocorrelation using fft, and 
when testing the code against numpy.correlate, I realised that I am not 
sure about the definition... There are various function related to 
correlation as far as numpy/scipoy is concerned:
   
    numpy.correlate
    numpy.corrcoef
    scipy.signal.correlate

    For me, the correlation between two sequences X and Y at lag t is 
the sum(X[i] * Y*[i+lag]) where Y* is the complex conjugate of Y. 
numpy.correlate does not use the conjugate, scipy.signal.correlate as 
well, and I don't understand numpy.corrcoef. I've never seen complex 
correlation used without the conjugate, so I was curious why this 
definition was used ? It is incompatible with the correlation as a 
scalar product, for example.

    Could someone give the definition used by those function ?

    cheers,

    David