Catalog Data:

483 Introduction to Digital Signal Processing (3, FaSp): Fundamentals of digital signal processing covering: discrete time linear systems, quantization, sampling, Z-transforms, Fourier transforms, FFTs and filter design. Prerequisite: EE 301a.

 

Text book:

A Course in Digital Signal Processing, Boaz Porat, John Wiley & Sons, 1996.

 

Course Coordinators:

Richard M. Leahy, Professor of Electrical Engineering

 

Topics:

Part 1: Signal Analysis
Class 1: Introduction and overview
Class 2: continuous time signals, Discrete time signals and Fourier analysis
Class 3: Sampling: aliasing, sampling theorem and signal reconstruction
Class 4: Practical signal reconstruction. Band-pass sampling.
Class 5: The discrete Fourier transform: definition and properties
Class 6: The discrete cosine transform (DCT) and other unitary transforms
Class 7: Fast Fourier transforms
Class 8: Relationships between the FT, DFT and DTFT, leakage, resolution
Class 9: Practical spectral analysis

 

Part 2: System Analysis
Class 10: LSI systems, causality and BIBO stability, impulse response
Class 11: Linear difference equations (LDEs) for LSI systems
Class 12: Z transform and its properties, system function
Class 13: Frequency response: magnitude and phase
Class 14: linear phase, minimum phase and all-pass systems
Class 15: Filter types: FIR, IIR, low pass, high pass, bandpass,
Class 16: differentiators, Hilbert transformers

Class 17: MIDTERM

 

Part 3: Filter Design and Implementation
Class 18: Linear phase FIR filters
Class 19: FIR filter design: least squares and window design methods
Class 20: FIR filter design: Chebyschev approximation
Class 21 Classical IIR designs
Class 22: Impulse invariance, bilinear transform and frequency transformation.
Class 23: IIR design using least squares
Class 24: Filter structures
Class 25: Quantization effects

 

Part 4: Other Topics and Applications (time permitting)
Class 26: Oversampling and sigma-delta converters.
Class 27: Sample-rate conversion
Class 28: Introduction to adaptive filtering

 

Course Objectives:

The objective of this course is to provide a basic introduction to the theory of digital signal processing (DSP). I assume a familiarity with the Fourier and Laplace transforms and concepts such as linearity and shift invariance that are used in the description and analysis of linear analog systems. Much of what we do extends these ideas to the field of discrete-time systems. Major parts of the course will concentrate on signal analysis using Fourier transforms, linear system analysis, Filter design and a few more advanced topics. In the first part of the course we will study the discrete Fourier transform and its properties. We will also study the sampling theorem and the relationship between continuous and discrete time transforms. We will see how discrete time, linear shift invariant systems can be characterized using linear difference equations and the impulse response and show how tools such as the z-transform and discrete Fourier transform can be used in the design and analysis of such systems. We will then study the design and implementation of digital filters. I will also try to include some topical material: how do 1-bit A/D converters work?, why is the DCT used in JPEG image compression?, what are adaptive filters? While this course deals largely with the theory of DSP, we will use a powerful software package, MATLAB, to look at applications of this theory, particularly Fourier analysis and digital filter design.

 

Course Outcomes:

The students will be able to:
1. Analyze signals and systems using the discrete time and discrete Fourier transforms. Understand the effects of windowing and zeropadding of data.
2. Determine appropriate antialiasing, sampling and reconstruction procedures to sample and reconstruct analog signals with finite bandwidth.
3. Understand how and why one would use other unitary transforms to represent discrete-time signals.
4. Analyze a discrete time system for linearity, stability, causality and shift invariance.
5. Transform the representation of linear shift invariant systems between linear difference equations, system functions, frequency response and impulse response.
6. Recognize and analyze the different basic digital filter types: low and high pass, bandpass and bandstop, differentiator, integrator, Hilbert transformer, IIR, FIR, linear phase, and minimum phase.
7. Design FIR linear phase filters to meet a given specification using Matlab with an understanding of the underlying principles of the different design methods including least squares and Chebyshev approximation.
8. Design IIR filters to meet a given specification using Matlab with an understanding of the underlying principles of the different design methods including transformation of classical analog prototypes using impulse invariance and bilinear transforms.
9. Understand the potential effects of coefficient quantization and system implementation on the performance of digital filters.
10. Understand the principles underlying oversampling techniques and one-bit (sigma-delta) A/D and D/A converters.
11. Solve DSP problems using the Matlab programming environment.

 

Projects:

Students complete 8-10 homeworks during the semester. 50% of these involve significant use of Matlab to solve filter design and signal analysis problems and to investigate the application of the material described to signal and image analysis.