JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Digital Signal Processing

Course Objectives

The main objectives of the course are:

• This course focuses on problems algorithms and solutions for processing signals in an manner that is responsive to a changing environment.
• To develop systems on recursive, model-based estimation methods taking the advantage of the statistical properties of the received signals.
• To analyze the performance of adaptive filters and considers the application of the theory to a variety of practical problems such as beam forming and echo cancellation signal.
• To understand innovation process, Kalman filter theory and estimation of state using the innovation process, concept of Kalman Gain and Filtering.

Course Outcomes

After studying the course, the student is expected to be able to :

• Design and apply optimal minimum mean square estimators and in particular linear estimators.
• Understand and compute their expected performance and verify it.
• Design, implement and apply Wiener Filters (FIR, non-casual, causal) and evaluate their performance.
• To understand innovation process, Kalman filter theory and estimation of state using the Innovation Process, concept of Kalman Gain and Filtering.
• Design, implement and apply LMS, RLS and Kalman filters to given applications.

UNIT - I

Introduction to Adaptive Systems: Definitions, Characteristics, Applications, Example of an Adaptive System. The Adaptive Linear Combiner - Description, Weight Vectors, Desired Response Performance function - Gradient & Mean Square Error.

UNIT - II

Development of Adaptive Filter Theory & Searching the Performance surface: Introduction to Filtering - Smoothing and Prediction – Linear Optimum Filtering, Problem statement, Principle of Orthogonally - Minimum Mean Square Error, Wiener- Hopf equations, Error Performance - Minimum Mean Square Error.

UNIT - III

Steepest Descent Algorithms: Searching the performance surface – Methods & Ideas of Gradient Search methods - Gradient Searching Algorithm & its Solution - Stability & Rate of convergence - Learning Curves Gradient Search by Newton’s Method, Method of Steepest Descent, Comparison of Learning Curves.

UNIT - IV

LMS Algorithm & Applications: Overview - LMS Adaptation algorithms, Stability & Performance analysis of LMS Algorithms - LMS Gradient & Stochastic algorithms - Convergence of LMS algorithm. Applications: Noise cancellation – Cancellation of echoes in long distance telephone circuits, Adaptive Beam forming.

R19 M.TECH. SYSTEMS AND SIGNAL PROCESSING

UNIT - V

Kalman Filtering: Introduction to RLS Algorithm, Statement of Kalman filtering problem, The Innovation Process, Estimation of State using the Innovation Process- Expression of Kalman Gain, Filtering Examples using Kalman filtering.

TEXT BOOKS:

• 1. Adaptive Signal Processing - Bernard Widrow, Samuel D. Strearns, PE, 2005.
• 2. Adaptive Filter Theory - Simon Haykin-, 4th Ed., PE Asia 2002.

REFERENCES:

• 1. Optimum signal processing: An introduction - Sophocles. J. Orfamadis, 2 Ed., McGraw-Hill, New York, 1988.
• 2. Adaptive signal processing-Theory and Applications, S. Thomas Alexander, Springer –Verlag, 1986.
• 3. Siganl analysis – Candy, Mc Graw Hill Int. Student Edition
• 4. James V. Candy, Signal Processing: A Modern Approach, McGraw-Hill, International Edition, 1988. R19 M.TECH. SYSTEMS AND SIGNAL PROCESSING M.TECH.- I YEAR- II SEMESTER SYSTEMS AND SIGNAL PROCESSING