Signal Processing for Communication Systems
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
Markov chains are useful in computing the probability of events that are observable. However, in many real world applications, the events that we are interested in are usually hidden, that is we don’t observe them directly. These hidden events need to be inferred. For example, given a sentence in a natural language we only observe the … Read more
Key focus: Markov chains are a probabilistic models that describe a sequence of observations whose occurrence are statistically dependent only on the previous ones. ● Time-series data like speech, stock price movements.● Words in a sentence.● Base pairs on the rung of a DNA ladder. States and transitions Assume that we want to model the … Read more
Exponential distribution PDF and CDF, memoryless property, mean/variance, and how to generate samples in Matlab or Python for queueing and fading models.
Binomial random variable, a discrete random variable, models the number of successes in $latex n$ mutually independent Bernoulli trials, each with success probability $latex p$. The term Bernoulli trial implies that each trial is a random experiment with exactly two possible outcomes: success and failure. It can be used to model the total number of … Read more
Bernoulli random variable is a discrete random variable with two outcomes – success and failure, with probabilities p and (1-p). It is a good model for binary data generators and also for modeling bit error patterns in the received binary data when a communication channel introduces random errors. To generate a Bernoulli random variable X, … 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.
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