Signal Processing for Communication Systems
Key focus: Discuss statistical measures for stochastic signals : mean, variance, skewness, kurtosis, histogram, scatterplot, cross-correlation and auto-correlation. Deterministic and stochastic signals A deterministic signal is exactly predictable for the given time span of interest. It could be expressed using analytic form (example: x(t) = sin (2 π fc t) ). Many of the signals … Read more
Key focus: Shown with examples: let’s estimate and plot the probability density function of a random variable using Python’s Matplotlib histogram function. This post contains interactive python code which you can execute in the browser itself. Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s … Read more
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.
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
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
Non-central chi-squared distribution: PDF with non-centrality parameter λ, relation to Rician power / energy detection, and Matlab/Python sampling examples.
What a chi-squared distribution is, how degrees of freedom shape the PDF, and how to sample/plot it in Matlab or Python — used in energy detection and confidence regions.
Uniform random variables are used to model scenarios where the expected outcomes are equi-probable. For example, in a communication system design, the set of all possible source symbols are considered equally probable and therefore modeled as a uniform random variable. The uniform distribution is the underlying distribution for an uniform random variable. A continuous uniform … Read more
Introduction to Probability: The Foundation of Random Signals In the world of communication engineering, “certainty” is a luxury we don’t have. From the thermal noise in your smartphone’s receiver to the fading of a satellite signal, every process we analyze is governed by uncertainty. Probability is the mathematical language that allows us to model … Read more