I am trying to apply a low pass Gaussian filter on a signal and find the exact location of maximum/minimum in the resulting smoothed signal. I have to do it for a few values of sigma (Gaussian bandwidth).
How is it possible to implement such Gaussian filtering and compensate phase shifts during filtering so that I can find the exact location of extrema as an index of signal location?
I have tried:
Convolution with a low pass Gaussian kernel (windowing) results in extension of resulting signal length which makes it impossible to find extremum as an index of original signal.
2) use of
Fourier transform on signal and kernel and multiplication in Fourier domain makes the resulting signal in time domain circulary shifted.