should be approximately the same. More precisely, in a maximum length sequence of length there are ones and zeros. The number of ones equals the number of zeros plus one, since the state containing only zeros cannot occur. Run property A "run" is a sub-sequence of consecutive "1"s or consecutive "0"s within the MLS concerned. The number of runs is the number of such sub-sequences. Of all the "runs" (consisting of "1"s or "0"s) in the sequence : One half of the runs are of length 1. One quarter of the runs are of length 2. One eighth of the runs are of length 3. ... etc. ... Correlation property The circular autocorrelation of an MLS is a Kronecker delta function (with DC offset and time delay, depending on implementation). For the ±1 convention, i.e., bit value 1 is assigned and bit value 0 , mapping XOR to the negative of the product: where represents the complex conjugate and represents a circular shift. The linear autocorrelation of an MLS approximates a Kronecker delta. 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[n] 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[n] and the MLS is s[n], then Taking the cross-correlation with respect to s[n] of both sides, and assuming that φss is an impulse (valid for long sequences) Any signal with an impulsive autocorrelation can be used for this purpose, but signals with high crest factor, such as the impulse itself, produce impulse responses with poor signal-to-noise ratio. It is commonly assumed that the MLS would then be the ideal signal, as it consists of only full-scale values and its digital crest factor is the minimum, 0 dB. However, after analog reconstruction, the sharp discontinuities in the signal produce strong intersample peaks, degrading the crest factor by 4-8 dB or more, increasing with signal length, making it worse than a sine sweep. Other signals have been designed with minimal crest factor, though it is