EEC201 - Digital Signal Processing
4 units - Winter Quarter
Lecture: 4 hours
Prerequisite:course 150B; Statistics 120 or Mathematics 131 or Mathematics 167 recommended.
Grading:Letter:Homework (10%); Midterm (20%); Course project (30%); Final Exam (40%).
Theory and design of digital filters. Classification of digital filters, linear phase systems, all-pass functions, FIR and IIR filter design methods and optimality measures, numerically robust structures for digital filters..
Expanded Course Description
- TOPICAL OUTLINE:
- Review of DSP Fundamentals
- Discrete-time signals and system definitions
- Linear time-invariant (LTI) systems, stability and causality of LTI systems
- Impulse response, convolution sum, discrete-time Fourier transform and Eigen functions
- Transform analysis of LTI systems: magnitude response, phase response and group delay
- Z-transform, rational functions, poles and zeros, region of convergence (ROC) and difference equations
- Digital Filters
- Transmission zeros
- Filter classification based on the magnitude response and phase response
- Generalized linear phase filters
- FIR generalized linear phase filter types and their properties
- The Digital Filter Design Problem
- Filter specifications
- Normalized magnitude response and db plots
- Wrapped and unwrapped phase response
- Optimality criteria for filter design
- FIR Filter Design Techniques
- Window method
- Optimal window design and the prolate spheroidal function
- Eigen filter approach
- Optimum equiripple approximation using FIR filters
- IIR Filter Design Techniques
- Working principle of IIR filters
- The bilinear transformation
- Butterworth, Chebyshev and Elliptic filters
- All pass filters and their properties
- The all pass decomposition
- Numerically Robust Structures for Digital Filters
- Direct forms, parallel form, cascade form
- The finite precision representation: quantizing the filter coefficients by truncation or rounding
- Roundoff noise analysis of filter structures
- Scaling and dynamic range analsysis of filter structures
- Lattice structures for all pass filters
- Applications of Digital Filtering
ADDITIONAL INFORMATION FOR STUDENTS: STATEMENT OF COURSE DESIGN PROJECT: The students are first introduced to the theoretical aspects of the digital filter design problem. They then study well established techniques for designing such filters and are presented with a generic framework for analyzing the performance of these filters when implemented with finite numerical precision. In the design project, students are encouraged to explore new applications and are therefore given the opportunity to use their acquired knowledge to optimize digital filters to best meet certain specifications and/or to minimize a specific error criterion. In these design problems, the student typically must choose between a number of alternatives in order to achieve the best performance under a set of constraints (implementation cost, error criterion, magnitude distortion, phase distortion, quantization effects ?. etc.). These design tasks involve both theoretical derivations and computer simulations and in almost all cases, do not have a unique solution. ADDITIONAL INFORMATION FOR STUDENTS: This class is a core graduate level course in Digital Signal Processing (DSP) and is essential for students planning to pursue research in this area. The goal of this class is to provide an in- depth treatment of the topic of digital filter design. In specific, the first part of the course covers the theoretical aspects of the digital filter design problem whereas the second part addresses the implementation of these filters via numerically robust structures. A filter design project where students can experiment with the inherent filter design tradeoffs and pursue novel applications in data compression, communications and genomics to name a few, is a key component of this class. By the end of the term, we hope to provide a thorough and unified treatment of digital filters and their role in contemporary applications to the level where the student can engage in research in these areas.
- Review of DSP Fundamentals
Reference: D. J. DeFatta, J. G. Lucas, and W. S. Hodgkiss, Digital Signal Processing: A System Design Approach, Wiley, 1988.
EXPLANATION OF POTENTIAL COURSE OVERLAP:EEC150B and EEC151 cover some of the same topics, but at much different levels. As a graduate level course, the overlapping topics are addressed in much more detail.
Last revised: 2/06