Abstract
This paper describes some properties of randomly sampled M-sequence, and compares those properties for two methods of sampling. The first method, called method I, is to sample ([k·wi]+1)'st bit from a k-tuple of an M-sequence, where wi is a random number having any distribution function between 0 and 1. The second method, called method II, is to sample ([k·Xi]+1)'st bit from a ([k·Xi]+1)-tuple of M-sequence, where Xi is a uniform random number between 0 and 1.
It is shown that the maximum value of the ensemble averaged autocorrelation function in case of method I becomes minimum when wi is a uniform random number. It is also shown that the maximum value of the ensemble averaged autocorrelation function of randomly sampled sequence generated by method II is smaller than that of the sequence generated by method I.
From these results, we see that method II is better than method I in order to get a binary random sequence having good random properties.
