Random Process

Bayes’ theorem

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Key focus: Bayes’ theorem is a method for revising the prior probability for specific event, taking into account the evidence available about the event. Introduction In statistics, the process of drawing conclusions from data subject to random variations – is called “statistical inference”. Usually, in any random experiment, the observations are recorded and conclusions have … Read more

Histogram to PDF in Matlab — normalize bins and overlay the theoretical curve

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Turn a Matlab histogram into an estimated PDF: normalize by sample count and bin width, then overlay normpdf / theoretical densities for Gaussian, Rayleigh, and exponential checks.

Generate multiple sequences of correlated random variables

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In the previous post, a method for generating two sequences of correlated random variables was discussed. Generation of multiple sequences of correlated random variables, given a correlation matrix is discussed here. Correlation Matrix Correlation matrix defines correlation among N variables. It is a symmetric $latex N \times N $ matrix with the $latex (ij)^{th} $ … Read more

Generate two correlated random sequences

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This article discusses the method of generating two correlated random sequences using Matlab. If you are looking for the method on generating multiple sequences of correlated random numbers, I urge you to go here. Generating two vectors of correlated random numbers, given the correlation coefficient $latex \rho $, is implemented in two steps. The first … Read more

BPSK Bit Error Rate in AWGN: Derivation and Simulation

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BPSK Lab path:Derive BER (theory) → AWGN noise model → BER simulation (Python & Matlab)Tools: BER vs Eb/N0 calculator · Shannon capacity The BPSK bit error rate for an optimum receiver in AWGN follows from a simple decision-threshold argument. This post derives it step by step, then checks the result with a Monte Carlo simulation … Read more