On filtered binary processes

The problem of calculating the probability density function of the output of an RC filter driven by a binary random process with intervals generated by an equilibrium renewal process is studied. New integral equations, closely related to McFadden's original integral equations, are derived and solved by a matrix approximation method and by iteration. Transformations of the integral equations into differential equations are investigated and a new closed-form solution is obtained in one special case. Some numerical results that compare the matrix and iteration solutions with both exact solutions and approximate solutions based upon the Fokker-Planck equation are presented.

[1]  H. E. McKean,et al.  Tables of the Incomplete Beta Function , 1968 .

[2]  James E. Mazo,et al.  On a nonlinear problem involving RC noise , 1973, IEEE Trans. Inf. Theory.

[3]  R. F. Pawula,et al.  The zero crossing variance of the smoothed random telegraph signal , 1975 .

[4]  J. A. McFadden,et al.  The Distribution of a Certain Nonlinear Functional of an Ornstein-Uhlenbeck Process , 1962 .

[5]  J. McFadden,et al.  The probability density of the output of an RC filter when the input is a binary random process , 1959, IRE Trans. Inf. Theory.

[6]  Robert F. Pawula,et al.  A differential equation related to a random telegraph wave problem--Computer calculation of series solution , 1987, IEEE Trans. Inf. Theory.

[7]  Jack Salz,et al.  A theorem on conditional expectation , 1970, IEEE Trans. Inf. Theory.

[8]  Robert F. Pawula,et al.  Theoretical and experimental results for the distribution of a certain nonlinear functional of the Ornstein-Uhlenbeck process , 1969, IEEE Trans. Inf. Theory.

[9]  R. F. Pawula,et al.  The probability density and level-crossings of first-order non-linear systems driven by the random telegraph signal† , 1977 .

[10]  A. G. Munford.  Moments of a filtered binary process , 1986, IEEE Trans. Inf. Theory.

[11]  John T. Rickard,et al.  The zero-crossing interval statistics of the smoothed random telegraph signal , 1977, Inf. Sci..

[12]  Richard Fitzhugh,et al.  Statistical properties of the asymmetric random telegraph signal, with applications to single-channel analysis , 1983 .

[13]  Lee D. Davisson,et al.  On the distribution and moments of RC -filtered hard-limited RC -filtered white noise , 1973, IEEE Trans. Inf. Theory.

[14]  W. M. Wonham,et al.  Probability Densities of the Smoothed ‘ Random Telegraph Signal ’† , 1958 .

[15]  Ian F. Blake,et al.  Level-crossing problems for random processes , 1973, IEEE Trans. Inf. Theory.

[16]  R. F. Pawfjla.  Statistical geometry of the smoothed random telegraph signal , 1972 .