Signal Processing for Communication Systems
Mathematical details of convolution, its relationship to polynomial multiplication and the application of Toeplitz matrices in computing linear convolution are discussed in the previous article. A short survey of different techniques to compute discrete linear convolution (with Matlab code) is given here. Definition Given an LTI (Linear Time Invariant) system with impulse response \(h[n]\) and … Read more
Cholesky decomposition is an efficient method for inversion of symmetric positive-definite matrices. Let’s demonstrate the method in Python and Matlab. Cholesky factor Any symmetric positive definite matrix can be factored as where is lower triangular matrix. The lower triangular matrix is often called “Cholesky Factor of ”. The matrix can be interpreted as square root … 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 generic complex baseband simulation technique, to simulate all M-ary phase shift keying (M-PSK) modulation techniques is given here. The given simulation code is very generic, and it plots both simulated and theoretical symbol error rates for all MPSK modulation techniques. M-ary phase shift keying (M-PSK) modulation In phase shift keying, all the information gets … Read more
The moving average filter is a simple Low Pass FIR (Finite Impulse Response) filter commonly used for smoothing an array of sampled data/signal. It takes samples of input at a time and takes the average of those -samples and produces a single output point. It is a very simple LPF (Low Pass Filter) structure that … Read more
Quadrature Phase Shift Keying (QPSK) is a form of phase modulation technique, in which two information bits (combined as one symbol) are modulated at once, selecting one of the four possible carrier phase shift states. The QPSK signal within a symbol duration \(T_{sym}\) is defined as where the signal phase is given by Therefore, the … Read more
Key focus: BPSK, Binary Phase Shift Keying, bpsk modulation, bpsk demodulation, BPSK matlab, BPSK python implementation, BPSK constellation BPSK – introduction BPSK stands for Binary Phase Shift Keying. It is a type of modulation used in digital communication systems to transmit binary data over a communication channel. In BPSK, the carrier signal is modulated by … Read more
Keyfocus: Fading channel models for simulation. Learn how fading channels can be modeled as FIR filters for simplified modulation & detection. Rayleigh/Rician fading. Introduction A fading channel is a wireless communication channel in which the quality of the signal fluctuates over time due to changes in the transmission environment. These changes can be caused by … Read more
Central Limit Theorem – What is it ? The central limit theorem (CLT) is a fundamental concept in statistics and probability theory that explains how the sum of independent and identically distributed random variables behaves. The theorem states that as the number of these variables increases, the distribution of their sum tends to become more … Read more
Keywords: maximum likelihood decoding, digital communication, data storage, noise, interference, wireless communication systems, optical communication systems, digital storage systems, probability, likelihood estimation, python Introduction Maximum likelihood decoding is a technique used to determine the most likely transmitted message in a digital communication system, based on the received signal and statistical models of noise and interference. … Read more