Analytical determination of autocorrelation and noise power density spectrum of randomly modulated pulse width square waves

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Virginia Polytechnic Institute

The Wiener theory of the minimum mean square error ·criterion is well furnished by knowing the autocorrelation function of the input to the linear system. This input signal is generally an additive mixture of a piecewise continuous message and a noise.

The problem considered in this paper is the determination of the autocorrelation function and also their power density spectrum of the noise component for the random base and height modulated square wave whose leading edges are periodic functions of time.

We note that the adopted probability density function for heights of random square wave have Gamma-Distribution Density Function. In addition to this distribution function, we consider the rectangular and Beta-density function on the base of square waves. In fact, the leading edges of most periodic-random base function can be simply described by using the rectangular and Beta-Density function.

Another matter under consideration is the visualization of the variations noise power density spectrum immersed in the masked signal (mixtured signal) with respect to the variance σ² and s² of Gamma and Beta-distribution, respectively.