Random Process Archives - GaussianWaves

Bayes’ theorem

Mathuranathan — Sat, 17 Apr 2021 13:48:29 +0000

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

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Statistical measures for stochastic signals

Mathuranathan — Sun, 02 Aug 2020 13:38:47 +0000

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

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Matplotlib histogram and estimated PDF in Python

Mathuranathan — Fri, 05 Jun 2020 08:28:31 +0000

Key focus: Shown with examples: let’s estimate and plot the probability density function of a random variable using Python’s Matplotlib histogram function. Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability ... Read more

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Hidden Markov Models (HMM) – Simplified !!!

Mathuranathan — Tue, 17 Mar 2020 05:08:35 +0000

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

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Markov Chains – Simplified !!

Mathuranathan — Fri, 06 Mar 2020 07:11:37 +0000

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

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Generate color noise using Auto-Regressive (AR) model

Mathuranathan — Wed, 04 Dec 2019 07:16:19 +0000

Key focus: Learn how to generate color noise using auto regressive (AR) model. Apply Yule Walker equations for generating power law noises: pink noise, Brownian noise. Auto-Regressive (AR) model An uncorrelated Gaussian random sequence can be transformed into a correlated Gaussian random sequence using an AR time-series model. If a time series random sequence is ... Read more

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Generating colored noise with Jakes PSD: Spectral factorization

Mathuranathan — Thu, 17 Oct 2019 06:16:55 +0000

The aim of this article is to demonstrate the application of spectral factorization method in generating colored noise having Jakes power spectral density. Before continuing, I urge the reader to go through this post: Introduction to generating correlated Gaussian sequences. In spectral factorization method, a filter is designed using the desired frequency domain characteristics (like ... Read more

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Generate correlated Gaussian sequence (colored noise)

Mathuranathan — Tue, 15 Oct 2019 06:43:03 +0000

Key focus: Colored noise sequence (a.k.a correlated Gaussian sequence), is a non-white random sequence, with non-constant power spectral density across frequencies. Introduction Speaking of Gaussian random sequences such as Gaussian noise, we generally think that the power spectral density (PSD) of such Gaussian sequences is flat.We should understand that the PSD of a Gausssian sequence ... Read more

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Exponential random variable – simulation & application

Mathuranathan — Fri, 26 Jul 2019 05:51:23 +0000

Introduction An exponential random variable (RV) is a continuous random variable that has applications in modeling a Poisson process. Poisson processes find extensive applications in tele-traffic modeling and queuing theory. They are used to model random points in time or space, such as the times when call requests arriving at an exchange, the times when ... Read more

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Binomial random variable using Matlab

Mathuranathan — Thu, 25 Jul 2019 06:57:14 +0000

Binomial random variable, a discrete random variable, models the number of successes in mutually independent Bernoulli trials, each with success probability . 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 bit errors in ... Read more

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