Generation of Pseudo-Gaussian Signals by Use of Weighted m-Sequence
Hiroshi Kashiwagi, Masato Sakata · Transactions of the Society of Instrument and Control Engineers · 1976
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.