To learn and understand the concepts of stationary and non-stationary random signals
and analysis & characterization of discrete-time random processes
To enunciate the significance of estimation of power spectral density of random processes
To introduce the principles of optimum filters such as Wiener and Kalman filters
To introduce the principles of adaptive filters and their applications to communication engineering
To introduce the concepts of multi-resolution analysis
UNIT I DISCRETE-TIME RANDOM PROCESSES 9
Random variables – ensemble averages a review, random processes – ensemble averages,
autocorrelation and autocovariance matrices, ergodic random process, white noise, filtering
random processes, spectral factorization, special types of random processes – AR, MA, ARMA
UNIT II SPECTRUM ESTIMATION 10
Bias and consistency, Non-parametric methods – Periodogram, modified-Periodogram –
performance analysis. Bartlett’s method, Welch’s method, Blackman-Tukey method. Performance
comparison. Parametric methods – autoregressive (AR) spectrum estimation – autocorrelation
method, Prony’s method, solution using Levinson Durbin recursion.
UNIT III OPTIMUM FILTERS 9
Wiener filters – FIR Wiener filter – discrete Wiener Hopf equation, Applications – filtering, linear
prediction. IIR Wiener filter – causal and non-causal filters. Recursive estimators – discrete Kalman
UNIT IV ADAPTIVE FILTERS 9
Principles and properties of adaptive filters – FIR adaptive filters. Adaptive algorithms – steepest
descent algorithm, the LMS algorithm – convergence. Applications of adaptive filtering – noise
cancellation, channel equalization.
UNIT V MULTIRESOLUTION ANALYSIS 8
Short-time Fourier transform – Heisenberg uncertainty principle. Principles of multi-resolution
analysis – sub-band coding, the continuous and discrete wavelet transform – properties.
Applications of wavelet transform – noise reduction, image compression.
At the end of the course, the student should be able to:
Articulate and apply the concepts of special random processes in practical applications
Choose appropriate spectrum estimation techniques for a given random process
Apply optimum filters appropriately for a given communication application
Apply appropriate adaptive algorithm for processing non-stationary signals
Apply and analyse wavelet transforms for signal and image processing based application