ndcastillo/Ergodic_Process_Demostration

Demonstration that a bit frame is configured in an Ergodic Process. The following development is related to the determination of the ensemble averages of a PCM signal. In an analytical way, the mean and autocorrelation of the signal modulated by coded pulses will be calculated, indicating if this process is Stationary in the Broad Sense; this is that it must meet the condition of having a constant mean and the autocorrelation must not depend on time. On the other hand, a program was implemented in the MATLAB software in which the ergodicity of the process related to the PCM signal was verified, from this In this way, it was possible to verify that the statistical averages of the process coincide with the temporal averages.

ErgodicProcess

Demonstration that a bit frame is configured in an Ergodic Process.

git clone git@github.com:ndcastillo/ErgodicProcess.git && cd ErgodicProcess && ls -alh

What are we trying to prove?

That mean for stationary process in a instanteous time is equal a mean of a realization, also that autocorrelation for a random variable is equal that autocorrelation for a realization. Therefore, this stationary process will be an ergodic process.

A total of 500 random bit frames (runs) are generated with a quantity of $1000 [bits] where the bit time is T_b=1 [ns]. The generation of the random bits is done with the Matlab function rand(), which is configured with a uniform distribution. In addition, a Amplitude Modulator block will be simulated to obtain values of ak={-1,+1}. With these conditions it is intended to observe the PCM system.

PCM signal.

This signal was generate with a random impulse train. Now, The P-NRZ was the Line code used, width Vpp = 2 [V].