Abstract
A new method for generating pseudo-Gaussian signals by use of a weighted m-sequence is proposed. This method utilizes the central limit theorem and the uniform distribution property of the weighted m-sequence signal. M-tuples obtained from an m-sequence which is generated by an n-stage shift register are weighted and summed up to obtain pseudo-Gaussian signals, where M≤n.
Skewness and kurtosis of the signal thus obtained are theoretically calculated and it is shown that when the number of M-tuples which are summed becomes large, the skewness and the kurtosis approach to those of the Gaussian signal, provided M is suitably chosen.
Digital simulations are carried out and it is shown that the signal obtained remains Gaussian after it passes through a low pass filter having a time constant of even fifty times as much as the clock period of the signal.
A simple pseudo-Gaussian signal generator of analog type is also proposed which consists of a shift register, a summing amplifier, a first order filter and a sample-hold circuit.
Three types of statistical tests are carried out for those signals obtainned in digital simulations and from the analog type signal generator to see how good they fit to a Gaussian distribution (skewness, kurtosis, x2 test). These tests show that the signals are considered to be Gaussian under the 0.01 significance level.
