Maximum length sequence
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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 pseudo random binary signal system identification software that can be represented by the shift registers i.
An MLS is also sometimes called an n-sequence or an m-sequence. MLSs are spectrally flatwith the exception of a near-zero DC term. Practical applications for MLS include measuring impulse responses e. 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 systemsand in the efficient design of some fMRI experiments . MLS are generated using maximal linear feedback shift registers.
An MLS-generating system with a shift register of length 4 is shown in Fig. It can be expressed using the following recursive relation:. As MLS are periodic and shift registers cycle through every possible binary value with the exception of the zero vectorregisters can be initialized to any state, with the exception of the zero vector. A polynomial over GF 2 can be associated with the linear feedback shift register.
It has degree of the length of the shift register, and has coefficients that are either 0 or 1, corresponding to the taps of the register that feed the xor gate. A necessary and sufficient condition for the sequence generated by a LFSR to be maximal length is that its corresponding polynomial be primitive.
MLS have the following properties, as formulated by Solomon Golomb. The occurrence of 0 and 1 in the sequence should be approximately the same. The number of ones equals the number of zeros plus one, since the pseudo random binary signal system identification software containing only zeros cannot occur.
Of all the "runs" in the sequence of each type i. A "run" is a sub-sequence of "1"s or "0"s within the MLS concerned. The number of runs is the number of such sub-sequences. The circular autocorrelation of an MLS is a Kronecker delta function   with DC offset and time delay, depending on implementation. 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 [ n ] by taking its circular cross-correlation with the MLS.
If the impulse response of a system is h [ n ] and the MLS is s [ n ], then. Any signal with an impulsive autocorrelation can be used for this purpose, but signals with high crest factorsuch as the impulse itself, produce impulse responses with poor signal-to-noise ratio.
From Wikipedia, the free encyclopedia. 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 systemsand in the efficient design pseudo random binary signal system identification software some fMRI experiments  Contents.
Fundamentals of General Linear Acoustics. A maximum-length sequence is a pseudo random binary signal system identification software sequence whose circular autocorrelation except for a small DC-error is a delta function. Proceedings of the IEEE. Retrieved from " https: Pseudorandomness Polynomials Binary sequences. All Wikipedia articles needing clarification Wikipedia articles needing clarification from Pseudo random binary signal system identification software Views Read Edit View history.