Extraction of Impulse Responses
If a linear time invariant (LTI) system's impulse response is to be measured using a MLS, the response can be extracted from the measured system output y by taking its circular cross-correlation with the MLS. This is because the autocorrelation of a MLS is 1 for zero-lag, and nearly zero (−1/N where N is the sequence length) for all other lags; in other words, the autocorrelation of the MLS can be said to approach unit impulse function as MLS length increases.
If the impulse response of a system is h and the MLS is s, then
Taking the cross-correlation with respect to s of both sides,
and assuming that φss is an impulse (valid for long sequences)
Read more about this topic: Maximum Length Sequence
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