Signal Processing for Communication Systems
Convolution operation is ubiquitous in signal processing applications. The mathematics of convolution is strongly rooted in operation on polynomials. The intent of this text is to enhance the understanding on mathematical details of convolution. Polynomial functions: Polynomial functions are expressions consisting of sum of terms, where each term includes one or more variables raised to … 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 $latex Z$ whose probability distribution function (PDF) is a standard normal distribution ($latex \mu=0$ and $latex \sigma^2=1$). Now, if the random variable is squared (a … Read more
Calculating the energy and power of a signal was discussed in one of the previous posts. Here, we will verify the calculation of signal power using Discrete Fourier Transform (DFT) in Matlab. Check here to know more on the concept of power and energy. The total power of a signal can be computed using the … Read more
Key focus: Clearly understand the terms: power and energy of a signal, their mathematical definition, physical significance and computation in signal processing context. Energy of a signal: Defining the term “size”: In signal processing, a signal is viewed as a function of time. The term “size of a signal” is used to represent “strength of … 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
Definition A random process (or signal for your visualization) with a constant power spectral density (PSD) function is a white noise process. Power Spectral Density Power Spectral Density function (PSD) shows how much power is contained in each of the spectral component. For example, for a sine wave of fixed frequency, the PSD plot will … Read more
[ratings] Researchers, working on Ultra-Parallel Visible Light Communications (UP-VLC) project, have demonstrated 3.5Gpbs free space data transmission via three separate micro-LEDs that emit red, blue and green colours. In effect, combining the three colours (that makes up for white colour), researchers say that achieving data rates over 10Gbps is feasible. The technology enabler here is … Read more
The goal of timing recovery is to estimate and correct the sampling instants and phase at the receiver, such that it allows the receiver to decode the transmitted symbols reliably. What is Symbol timing Recovery : When transmitting data across a communication system, three things are important: frequency of transmission, phase information and the symbol … Read more
As discussed in the introduction to estimation theory, the goal of an estimation algorithm is to give an estimate of random variable(s) that is unbiased and has minimum variance. This criteria is reproduced here for reference $latex E\left\{\hat{f}_0 \right\} = f_0 &s=1$ $latex \sigma^{2}_{\hat{f}_0}= E \left\{ ( \hat{f}_0 – E [ \hat{f}_0 ] )^2 \right\} … Read more
[ratings] In a given communication system, we always want to send data that represent real world data representing some physical quantity (be it speech, temperature, etc..,) .The real world physical quantity exist in analog domain and it becomes imperative to convert it to digital domain if we want to send it via a digital communication … Read more