Signal Processing for Communication Systems
Key focus: Learn how to plot FFT of sine wave and cosine wave using Matlab. Understand FFTshift. Plot one-sided, double-sided and normalized spectrum. Introduction Numerous texts are available to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT). Often we are confronted with the need to generate … 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
Generating a continuous signal and sampling it at a given rate is demonstrated here. In simulations, we may require to generate a continuous time signal and convert it to discrete domain by appropriate sampling. For baseband signal, the sampling is straight forward. By Nyquist Shannon sampling theorem, for faithful reproduction of a continuous signal in … Read more
Power delay profile gives the signal power received on each multipath as a function of the propagation delays of the respective multipaths. Power delay profile (PDP) A multipath channel can be characterized in multiple ways for deterministic modeling and power delay profile (PDP) is one such measure. In a typical PDP plot, the signal power … Read more
Understand various characteristics of a wireless channel through multipath channel models. Discuss Wide Sense Stationary channel, uncorrelated scattering channel, wide sense stationary uncorrelated scattering channel models and scattering function. Introduction Wireless channel is of time-varying nature in which the parameters randomly change with respect to time. Wireless channel is very harsh when compared to AWGN … Read more
Why BLUE : We have discussed Minimum Variance Unbiased Estimator (MVUE) in one of the previous articles. Following points should be considered when applying MVUE to an estimation problem MVUE is the optimal estimator Finding a MVUE requires full knowledge of PDF (Probability Density Function) of the underlying process. Even if the PDF is known, … Read more
Key focus: Understand step by step, the least squares estimator for parameter estimation. Hands-on example to fit a curve using least squares estimation Background: The various estimation concepts/techniques like Maximum Likelihood Estimation (MLE), Minimum Variance Unbiased Estimation (MVUE), Best Linear Unbiased Estimator (BLUE) – all falling under the umbrella of classical estimation – require assumptions/knowledge … Read more
The agenda for the subsequent series of articles is to introduce the idea of autocorrelation, AutoCorrelation Function (ACF), Partial AutoCorrelation Function (PACF) , using ACF and PACF in system identification. Introduction Given time series data (stock market data, sunspot numbers over a period of years, signal samples received over a communication channel etc.,), successive values … Read more
If a time series data is assumed to be following an Auto-Regressive (AR(N)) model of given form, the natural tendency is to estimate the model parameters a1,a2,…,aN. Least squares method can be applied here to estimate the model parameters but the computations become cumbersome as the order N increases. Fortunately, the AR model co-efficients can … Read more