Abstract:
This Report presents a brief review of uniform continuous density functions, both un-truncated and truncated, which are well described in existing literature. Then the discrete density function is derived and expressed in terms of Dirac’s delta functions and related mean and variance are derived and analyzed. The necessity of having truncated discrete density function, from the application point of view in communication systems, for example, is explained and related density and distribution functions are derived. For these functions, the mean and variance are expressed as functions of the length of the defined truncation interval and compared with related moments of the continuous truncated density function. The important advancement is achieved by deriving the truncated discrete density functions and expressing them in terms of Dirac’s delta and unit step functions. In this way it became possible to solve integrals which contain these density and distribution functions. Analyses of density functions with zero mean are repeated in the Appendix 1 for the case when the mean has a finite value.