This course covers important topics that have frequent and major applications in engineering fields such as radar communication, digital communication, speech and image processing, and array processing. The course provides a comprehensive analysis of signal processing algorithms for modeling of discrete time deterministic and random signals, Optimum filters design, power spectrum estimation of random signals, and implementation of adaptive filters. The course provides the framework of filter design as optimization problem and signal modeling based on the input-output relation of filters. It also cast a number of important applications such as estimation of signal from its noisy version, single-step and multi-step linear prediction of signal in noisy environment, deconvolution, and noise cancellation in the filtering frame work. The course treats specific topics such as review of random process, parametric signal modeling (Pade approximation, Prony's method, ARMA models, and AR model), Wiener and Kalman filtering, Non-Parametric and parametric spectrum estimation, and FIR & IIR adaptive filtering.