I consider a model used in many communication systems where the sum of n stochastic sinusoidal signals, each with general random amplitudes as well as phase angles is present. The exact probability distribution of the resulting signal’s amplitude is of particular interest in many important applications, however the general problem has remained open. I use probabilistic methods to prove new form...

1 Probability distribution functions Probability distribution functions assign probabilities to each of the possible outcomes of a random experiment. These distributions can be continuous (e.g. grading on a 4.0 scale), or discrete (e.g. grading with letter grades) (see Fig. ??). Figure 1: Terminology for continuous and discrete probability distributions. A probability distribution function spec...

1 Probability distribution functions Probability distribution functions assign probabilities to each of the possible outcomes of a random experiment. These distributions can be continuous (e.g. grading on a 4.0 scale), or discrete (e.g. grading with letter grades) (see Fig. 2). Figure 1: Terminology for continuous and discrete probability distributions. A probability distribution function speci...

We introduce and discuss the concept of Gaussian probability density function (pdf) for the n-dimensional hyperbolic space which has been proposed as an environment for coding and decoding signals. An upper bound for the error probability of signal transmission associated with the hyperbolic distance is established. The pdf and the upper bound were developed using Poincaré models for the hyperb...

1 Probability distribution functions Probability distribution functions assign probabilities to each of the possible outcomes of a random experiment. These distributions can be continuous (e.g. grading on a 4.0 scale), or discrete (e.g. grading with letter grades) (see Fig. 2). Figure 1: Terminology for continuous and discrete probability distributions. A probability distribution function speci...

In this paper Maximal Ratio Combining (MRC) technique over Rayleigh fading channel is described and some statistical characteristics of received signal envelope are analyzed. For analytical and numerical evaluation of system performance, the probability density functions (pdf) of received signal envelope after MRC are analyzed like particular solutions of corresponding differential equation, wh...

Aerodynamic damping for MEMS resonators is studied based on the numerical solution of Boltzmann-ESBGK equation. A compact model is then developed based on numerical simulations for a wide range of Knudsen numbers. The damping predictions are compared with both Reynold equation based models and several sets of experimental data. It has been found that the structural damping is dominant at low pr...