Convolution - Massive spike in noise section I am computing the correlation with MATLAB using the convolution fonction with a signal flipped before feeded into the function. Here are the results.



The first plot is the actual signal, the second one is the signal I am trying to find in the first signal and the third one is the convolution results. On the first plot, we can see at $n=3000$ and more  that the signal we are searching for is there and it is confirm by the spike in the third plot at $n = 3370$. However, there is massive spike in the beginning of the convolution (plot #3/ $n &lt; 3000$) even if the beginning of the first signal is noise (plot #1/ $n &lt; 3000$) . Why is there such spike in the convolution plot.
If your searched-for signal is partially similar to itself at some offset, that can also show up when correlated against an actual input signal containing it.  

Test your searched-for signal by autocorrelation against itself to check for this problem.  If you want a sharp convolution peak against test input, you need a searched-for signal that has very low self-similarity at any lag.