Why is not cross-correlation symmetric with respect to zero?

Hello! /p I need to create a harmonic signal, then to add some noise and to calculate auto cross-correlation. I know that auto cross-correlation must be symmetric with respect to zero. In two following pictures there are my code and the result that I get. How can I make it symmetric?

Answer 1

[Image Analyst]

When you cross correlate, the final signal length is the sum of the two signal length. You'll need to keep track of where the "zero" x location is. Like for the main signal, if it's centered about x=0 and has N elements, then the x=0 location is around N/2. So for your x array, x(1) is really -N/2 and x(N) is really N/2. Same concept for cross correlation. If both your signals are symmetric with respect to x, then your final signal will go from -(N+M)/2 at x(1) to +(N+M)/2 at the final element x(end).