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. 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
Key focus: With examples, let’s estimate and plot the probability density function of a random variable using Matlab 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 density function … Read more
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 matrix with the element equal to the correlation coefficient between the … 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 , is implemented in two steps. The first step is … Read more
If squares of k independent standard normal random variables are added, it gives rise to central Chi-squared distribution with ‘k’ degrees of freedom. Instead, if squares of k independent normal random variables with non-zero means are added, it gives rise to non-central Chi-squared distribution. Non-central Chi-square distribution is related to Ricean distribution, whereas the central … Read more
A random variable is always associated with a probability distribution. When the random variable undergoes mathematical transformation the underlying probability distribution no longer remains the same. Consider a random variable whose probability distribution function (PDF) is a standard normal distribution ( and ). Now, if the random variable is squared (a mathematical transformation), then the … Read more
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
Random Variable: In a “coin-flipping” experiment, the outcome is not known prior to the experiment, that is we cannot predict it with certainty (non-deterministic/stochastic). But we know the all possible outcomes – Head or Tail. Assign real numbers to the all possible events (this is called “sample space”), say “0” to “Head” and “1” to … Read more