how to calculate cross correlation of transient signal?
Correct speech signal is non-stationary. Hence, you have to stop here as whole dsp is based on stationary assumption, as of now at least to a larger extent. But as we cannot sit idle, we go ahead with quasi-stationary assumption. Take a window (rect/hamming/hanning - these have trade-offs) of 20-30 msec (this is different for male/female/music and is taken as 3-4 pitch periods in speech signal, you can keep it fixed at 30 msec (also referred as narrowband speech processing to get an intuition). Using this window break the speech signal into frames by windowing and shifting the window and extracting a frame for every window. You now have a bag of window length vectors of the given speech signal. Find auto-corr of these for any further processing as within the window the signal is assumed to be stationary (! though not exactly but better than the whole signal).