Correlation of two signals at different sample rate I have a signal $X$ and I want to find signal $Y$ in $X$, I can achieve this by cross-correlation. Signal $X$ is sampled at $8000\textrm{ Hz}$, and $Y$ signal is sampled at $44100\textrm{ Hz}$. 

My question is "should both signals be sampled at same rate to correlate to find $Y$ in $X$ " Or is it okay to correlate two signals sampled at different rate to find  $Y$ in $X$?
If you are looking for the exact signal, then yes you need to resample one of them to the same rate as the other before performing a cross correlation. Otherwise you will be cross correlating against a time-stretched (or compressed) version of the desired signal (which probably will not yield accurate results). If your $Y$ signal bandwidth is less than $4000\textrm{ Hz}$, then you may want to use an anti-aliasing filter and resample it to $8000\textrm{ Hz}$ for reduced computational load in the cross correlation. If not, then you must resample the signal $X$ to $44100\textrm{ Hz}$ in order for a cross correlation to be meaningful.