Q:

How to discard the first spike after auto-correlation and handle sloping auto-correlation output

Disclaimer: I am not very mathematically inclined and am mostly looking to be pointed in the right direction.
I have various signals that I am putting through an auto-correlation function that uses two DFTs. The output of auto-correlation of two of those signals is shown below.

I am looking to discard the initial spike in the case of Signal1, and I am looking for a way to handle the slope of Signal 2. Both of these are necessary since I am using a simple max function to determine the highest spike, but this doesn't work with the inclusion of the smaller lags and downward sloping correlations.
-Since I am using two DFTs, is there some way for me to use the output from the first to trim the output of the auto-correlation?
-Is there some way for me to trim some frequencies to avoid downward sloping outputs?
-Is there something better than the max function that will solve both of these problems?
I'd greatly appreciate any information anyone has on solving these problems.

A:

I found the solution. Thank you to Glen_b whose comments helped me see what needed to be fixed with my approach.
A major issue with my data was that I wasn't centering it before putting it through my auto-correlation function. This (I assume) is why the output of my auto-correlation function was always positive, and never negative as Glen_b suggested it should be. While it is still not between 1 and -1, it is much closer to a real correlation now. After fixing this, I discovered that my "normalization" function (not actually normalization, I just am still not sure exactly what it does) makes a significant difference to the output of the graph.
After applying this shift to all points after correlation on centered data, my two graphs now look like shown bellow. (note: the x axis has been divided by 3, so a peak at 1500 on the originals would coincide with the peak at 500 on the new)

With this, my two problems are solved. I can trim the first spike by only looking at values that exist beyond the first negative correlation, and the output is now even with the x axis.
Edit: After testing on the rest of my data, it seems that in about 20% of my cases the outputs do not go negative after the first spike. Regardless, this has still been a major improvement.

