A SIGNAL-PROCESSING METHOD FOR EVALUATING A CONTINUOUS-LEVEL PROBABILITY FUNCTION-BASED ON FEW SAMPLED-DATA WITH ROUGHLY DIGITIZED LEVEL - AN APPLICATION OF Z-TRANSFORM AND NUMERICAL LAPLACE TRANSFORM

In the evaluation of the total structure of the non-Gaussian random no ise observed in the real environment, it often happens that not only t he mean and the variance of the fluctuation but also the whole probabi lity distribution should be estimated as reasonably as possible, based on a few number of sampled data with a rough quantization level. This paper notes the following property. The mean, the variance, and the h igher-order moments once evaluated by the averaging operation of the s ampled data are more stable and reliable than the individual frequency curve derived directly from the sampled data. Furthermore, by utilizi ng the saturation property of the cumulative probability distribution, a new method is presented to estimate the probability distribution of the original continuous level. More precisely, the probability distri bution for the quantized level is represented by a nonparametric Z-tra nsform suited to the theoretical evaluation of the statistical moments . The inverse Laplace transform is applied to the first-order hold int erpolation of the obtained Z-transform representation and the continuo us level distribution is estimated. More precisely, the series expansi on form is terminated as an approximation and the result is smoothed. Then the numerical inverse Laplace transform is applied using FILT. Fi nally, the proposed method is applied to the data with exponential or Erlang distribution generated by a simulation using the random variabl e, and the validity of the principle is verified. The method also is a pplied to the actual environmental noise, and the practical usefulness is verified.