A maximum length sequence (MLS) is a type of pseudorandom binary sequence.
They are bit sequences generated using maximal linear-feedback shift registers and are so called because they are periodic and reproduce every binary sequence (except the zero vector) that can be represented by the shift registers (i.e., for length-m registers they produce a sequence of length 2m − 1). An MLS is also sometimes called an n-sequence or an m-sequence. MLSs are spectrally flat, with the exception of a near-zero DC term.
These sequences may be represented as coefficients of irreducible polynomials in a polynomial ring over Z/2Z.
Practical applications for MLS include measuring impulse responses (e.g., of room reverberation or arrival times from towed sources in the ocean[1]). They are also used as a basis for deriving pseudo-random sequences in digital communication systems that employ direct-sequence spread spectrum and frequency-hopping spread spectrum transmission systems, and in the efficient design of some fMRI experiments.[2]
^Gemba, Kay L.; Vazquez, Heriberto J.; Fialkowski, Joseph; Edelmann, Geoffrey F.; Dzieciuch, Matthew A.; Hodgkiss, William S. (October 2021). "A performance comparison between m-sequences and linear frequency-modulated sweeps for the estimation of travel-time with a moving source". The Journal of the Acoustical Society of America. 150 (4): 2613–2623. Bibcode:2021ASAJ..150.2613G. doi:10.1121/10.0006656. PMID 34717519. S2CID 240355915.
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