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One of the properties of convolution is that the centroids of the functions being convolved should add. See equation (18) of Wolfram Alpha's section on convolution Convolution Properties. … For example, if we have a Gaussian centered at t1=300, and we convolute it another Gaussian centered at t2=200, the resulting Gaussian peak after convolution is centered at 500. …

In the linear convolution of two equal length sequences M and N, the length of the output is length(A)+length(B)-1, and if we apply the DFT property of converting convolution into multiplication, the output … is equal Max (length (M) or length (N)). a) If there a simple way to predict how many edge points are contaminated by circular convolution if we were interested in extracting only the linear convolution …

Circular Convolution on avoiding circular convolution by FFT, it was shown that the FFT length for convolution purposes set should be = (data set 1)+ (data set 2) -1. … The convolution length would be 2001. What is the correct approach for discarding the ends of a convolution? …

Since this is a convolution, I am wondering that by convolution theorem, one should be able to obtain identical results in Fourier domain, because convolution should become multiplication in the Fourier …

In convolution, the horizontal centroids add. … This time the delta is at t, and the Lorentzian is centered at $\mu$, the resulting convolution should be at t+$\mu$, but still the deltas do not shift. …

What is somewhat confusing is that they suggestion for the discrete convolution analogue of the continuous convolution, we should wrap the negative time section of the response function to the extreme … It seems the authors are suggesting circular shifting the zero centered response by N/2 (N is even) to get an equivalent convolution to continuous convolution. …

Consequently, the peaks in the signal will not shift their positions after convolution. The shortcut is to center the Gaussian at the mean (a,b)+dt/2, where dt is a sampling interval. …

There is a recent paper in a journal called ACS Measurements which suggests an alternative window for the sinc function (Why and How Savitzky–Golay Filters Should Be Replaced) Link: Open Access Paper. …

I was reading that convolution achieved via FFT is essentially a circular one. … If our desire is to get a linear convolution, how do we ensure that the output is a linear convolution, i.e., how many end points should be rejected from both ends after inverse FFT? …