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: Learn how to generate color noise using auto regressive (AR) model. Apply Yule Walker equations for generating power law noises: pink noise, Brownian noise. Auto-Regressive (AR) model An uncorrelated Gaussian random sequence can be transformed into a correlated Gaussian random sequence using an AR time-series model. If a time series random sequence is … Read more
The aim of this article is to demonstrate the application of spectral factorization method in generating colored noise having Jakes power spectral density. Before continuing, I urge the reader to go through this post: Introduction to generating correlated Gaussian sequences. In spectral factorization method, a filter is designed using the desired frequency domain characteristics (like … Read more
Key focus: Colored noise sequence (a.k.a correlated Gaussian sequence), is a non-white random sequence, with non-constant power spectral density across frequencies. Introduction Speaking of Gaussian random sequences such as Gaussian noise, we generally think that the power spectral density (PSD) of such Gaussian sequences is flat.We should understand that the PSD of a Gausssian sequence … 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
Key focus: Can a unique solution exists when solving ARMA (Auto Regressive Moving Average) model ? Apply minimization of squared error to find out. As discussed in the previous post, the ARMA model is a generalized model that is a mix of both AR and MA model. Given a signal x[n], AR model is easiest … Read more
Key focus: AR, MA & ARMA models express the nature of transfer function of LTI system. Understand the basic idea behind those models & know their frequency responses. Introduction Signal models are used to analyze stationary univariate time series. The goal of signal modeling is to estimate the process from which the desired signal is … Read more