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Maximum length sequence - Extraction of impulse responses | | Maximum length sequence - Extraction of impulse responses: Encyclopedia II - Maximum length sequence - Extraction of impulse responses | | If a LTI system's impulse response is to be measured using a MLS, the response can be extracted from the measured system output y(n) by taking its cross-correlation with the MLS sequence. 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 sequence length increases.
If the impulse response of a system is h ...
See also:Maximum length sequence, Maximum length sequence - Generation of maximum length sequences, Maximum length sequence - Extraction of impulse responses | | | Maximum length sequence, Maximum length sequence - Extraction of impulse responses, Maximum length sequence - Generation of maximum length sequences, Impulse response, Frequency response, Polynomial ring | | |
| | | Maximum length sequence: Encyclopedia II - Maximum length sequence - Extraction of impulse responses
Maximum length sequence - Extraction of impulse responses
If a LTI system's impulse response is to be measured using a MLS, the response can be extracted from the measured system output y(n) by taking its cross-correlation with the MLS sequence. 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 sequence length increases.
If the impulse response of a system is h(n) and the MLS is s(n), then
Taking the cross-correlation with respect to s(n) of both sides,
φsy = h(n) * φss
and assuming that φss is an impulse (valid for long sequences)
Other related archivesFrequency response, Impulse response, Polynomial ring, autocorrelation, binary sequence, feedback, impulse responses, periodic, polynomial rings, pseudo-random, reverberation, shift registers, signal-to-noise ratio
 Adapted from the Wikipedia article "Extraction of impulse responses", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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