Statistical properties of smoothed maximal-length linear binary sequences

The paper investigates the autocorrelation function, power spectrum and amplitude probability-density distribution of the output of a simple low-pass smoothing filter when a maximal-length linear binary sequence is applied at the input to the filter. Theoretical expressions are given for the autocorrelation function and power spectrum of the output in terms of the bandwidth of the smoothing filter and are applicable for any general maximal-length linear binary sequence. A technique is presented for determining the amplitude probability-density distribution of the filter output for a particular maximal-length linear binary sequence, and the deviation of this distribution from a Gaussian distribution is investigated as the bandwidth of the smoothing filter is varied. Experimental results verify the theoretical predictions.