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
Famous quotes containing the words extraction, impulse and/or responses:
“Logic is the last scientific ingredient of Philosophy; its extraction leaves behind only a confusion of non-scientific, pseudo problems.”
—Rudolf Carnap (1891–1970)
“Decisive inventions and discoveries always are initiated by an intellectual or moral stimulus as their actual motivating force, but, usually, the final impetus to human action is given by material impulses ... merchants stood as a driving force behind the heroes of the age of discovery; this first heroic impulse to conquer the world emanated from very mortal forces—in the beginning, there was spice.”
—Stefan Zweig (18811942)
“Research shows clearly that parents who have modeled nurturant, reassuring responses to infants’ fears and distress by soothing words and stroking gentleness have toddlers who already can stroke a crying child’s hair. Toddlers whose special adults model kindliness will even pick up a cookie dropped from a peer’s high chair and return it to the crying peer rather than eat it themselves!”
—Alice Sterling Honig (20th century)