INVESTIGACIÓN DEL PROCEDIMIENTO DE DOS ALGORITMOS DE MUESTREO-RECONSTRUCCIÓN DE PROCESOS GAUSSIANOS NO-DIFERENCIABLES

Abstract

One of the main problems in the study of the communications theory is the reconstruction of the achievements of the random processes from many samples using Models of Differential Processes. However, there is not enough investigation about reconstruction of random processes since the models of Non-Differential Processes. In the present work, the investigation of the Stationary Non- Differential Gaussian Processes is carried out as well as characterizing and comparing with the common Differential Processes. Also, the investigation about Sampling-Reconstruction Procedure of the Stationary Gaussian Random Processes will be realized using the Conditional Mean Rule considering different covariance functions, to reconstruct this kind of processes from a limited number of samples, evaluating its reconstruction function, error function and average error inside the interpolation zone. Moreover, the researching of the methodology of sampling-reconstruction procedure based on conditional mean rule is not applied to reconstruct and assess the realizations between samples with zero amplitude, that is, the realization zero crossing . Recently there is research related with some strategies of sampling-reconstruction procedure taking into account the realizations zero crossing; however researchers on this topic do not consider statistics features in order to be analyzed. For this reason the elicitation results for the methodology based on the two reconstruction algorithms implementation (optimal and no optimal), where each algorithm obtain only one realization of the process and so attempts to obtain the realization zero crossing to applied the samplingreconstruction procedure will be proposed. One of the techniques used to estimating of zero crossing is using a non-lineal converter (clipper), the same that contains the information about of zero crossing on its edges. On the other hand, no optimal algorithm attempts to reconstruct the realization of the process to the no lineal converter output. The methodology to the obtaining of the results is based into the implementation of two reconstruction algorithms (Optimal and No-Optimal), where each algorithm obtains single realization of the process, and attempts to get the zero crossing of the realization to finally implementing the procedure of sampling-reconstruction. Finally, the reconstruction function and reconstruction error function will be evaluated and compared among the different model processes. Some of the models of Non-Differentials Gaussian Processes used in this work are: RC-Stage Filter, Coupled Filter, Filter for Voice Model and Resonant RLC Filter.