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 … 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
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
How to simulate white noise in Matlab, check spectrum and power, and relate AWGN variance to SNR — with links to AWGN generation and BER tools.
Digital Modulations Lab path:BPSK → QPSK → M-PSK simulation → QPSK symbol timing → π/2-BPSK (5G NR)Tools: BER vs Eb/N0 · EVM → SNR · OFDM CP overhead 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 … Read more
Log-distance / log-normal shadowing path loss: formula beyond Friis, path-loss exponent by environment, shadowing χ, and how it extends free-space models.
Friis transmission equation and free-space path loss: $latex (4\pi d/\lambda)^2$, dB form, assumptions, and when to move to log-distance or two-ray models.
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Let’s review indexing techniques in Matlab: Indexing one dimensional array, two dimensional array, logical indexing, reversiong a vector – are covered. Consider a sample vector in Matlab. Index with single value Index with range of values Select a range of elements using ‘:’ operator. Example: Select elements with index ranging from 1 to 5. Making … Read more