Given a signal $x(t)$, how do I implement a form of autocorrelation function defined as $a(t,T) = x(t-T)x(t+T)$, where $T$ is an arbitrary constant?
(a fast implementation would be ideal)
Edit: This kind of signal I came across from seeing a "Parametric Symmetric Autocorrelation function", defined as above.
It is used in time-frequency analysis methods like WVD,...etc. $ R(t,\tau) = x(t + \frac{\tau}{2})x^{*}(t-\frac{\tau}{2})$
Thus far, I have implemented the steps as below for an example chirp: but the output of the fft2 at the end is wrong. (not a correct frequency)
At the output of the autocorrelation function (the PSIAF variant):
The final output of the LVD is wrong (should be point like):
Solved: Will look at using some of the already published C codes as per answer below to compute the $ R(t,\tau) $