CS-570

Statistical Signal Processing

Postgraduate

This course focuses on problems, algorithms, and solutions for processing signals in a manner that is responsive to a changing environment. Adaptive signal processing systems are developed which take advantage of the statistical properties of the received signals. The course analyzes the performance of adaptive filters and considers the application of the theory to a variety of practical problems such as interference and echo cancellation, signal and system identification, and channel equalization. The class is designed as an advanced statistical signal processing course in which students will build a strong foundation in approaching problems in such diverse areas as acoustic, sonar, radar, geophysical, biomedical, and communications signal processing. Understanding of the theoretical foundations of statistical and adaptive signal processing theory is achieved through a combination of theoretical and computer-based homework assignments.
Course Outline:
PART I: BACKGROUND MATERIAL AND LINEAR OPTIMUM FILTERING Topic 1: Background Material: Adaptive filtering - Concepts and applications; Discrete-time signal processing; Stationary processes and models; Spectrum analysis; Linear algebra - Eigenanalysis and matrix decompositions. Topic 2: Wiener Filtering: Minimum mean square error (MMSE) and the orthogonality principle; Digital Wiener filter and Wiener-Hopf equations; Constrained linear MMSE estimation; Applications - Minimum variance beamforming. Topic 3: Linear Prediction: Forward and backward prediction; Levinson-Durbin algorithm; Lattice filters; Applications - DPCM speech coding.
PART II: ADAPTIVE FILTERING METHODS Topic 4: Stochastic Methods: Steepest Descent algorithm; Least-MeanSquare (LMS) algorithm; Properties of the LMS; Normalized and frequency-domain LMS; Gradient adaptive lattice methods; Recursive LMS (RLMS) for adaptive IIR filtering; Applications - Active noise control and echo cancellation. Topic 5: Least Squares Methods: Least squares and orthogonality; Recursive least squares adaptive algorithms; Properties of RLS; Applications - ADPCM speech encoding.

LEARNING OUTCOMES
1. Knowledge: Having attended and succeeded in the course, the student is able to understand, analyze and design adaptive signal processing techniques for processing data and signals in a probabilistic framework.
2. Understanding: Having attended and succeeded in the course, the student has understood the basic principles of designing statistical signal processing algorithms and data analysis systems for handling scientific measurements.
3. Application: Having attended and succeeded in the course, the student is able to to develop innovative techniques on practical problems including interference and echo cancellation, signal and system identification, and channel equalization. Students  build a strong foundation in approaching problems in such diverse areas as acoustic, sonar, radar, geophysical, biomedical, astrophysical and communications signal processing.
4. Analysis: Having attended and succeeded in the course, the student is able to combine mathematical, statistical and adaptive techniques for problem solving, analyze advanced data processing systems using a suite of performance measures, and employ novel analysis methods in various scientific fields.
5. Synthesis: Having attended and succeeded in the course, the student is able to design new data processing strategies, and combine deterministic with statistical, model-based with data-driven  methods for extracting information from scientific data.
6. Evaluation: Having attended and succeeded in the course, the student is able to compare the performance of different signal processing methods, utilize measurable performance criteria, and evaluate the efficiency of state of the art algorithms.

STUDENT PERFORMANCE EVALUATION
Class attendance/participation
Exercises/projects
Oral/written exams
 
Homeworks: 10%
Project: 30%
Midterm exam: 25%
Final exam: 35%
 

6

CS-370, CS-217

http://www.csd.uoc.gr/~hy570