Hal H. Ottesen

EE 4541 Digital Signal Processing I
This course opens the gate to the many graduate courses offered in Digital Signal Processing. Reviews the continuous systems and Laplace transforms. Then discrete signals and systems are covered with the z-transforms and its inverse. Finally, time-domain and frequence-domain analysis of discrete transfer functions are discussed.

Review of discrete signals and systems. The use and applications of the discrete-time Fourier transforms (DTFT), the discrete Fourier transforms (DFT) and fast Fourier transform (FFT) are discussed. Design of analog and digital Butterworth filters, like highpass, lowpass, bandpass, and bandstop, via frequency transformations and bilinear transforms. Finite impulse response (FIR) filter design with linear phase using fixed windows, like Hamming, Hanning, Blackman, etc., and the variable Kaiser window. Interpolation and decimation techniques. Effects of quantizing. By the end of the course, the students will be proficient in analyzing digital systems and designing filters using the software program Matlab.

Digital Signal Processing II
Prerequisite DSP I and a knowledge of Matlab or equivalent. Covers analog and digital design of Chebyshev, elliptic, and allpass filters. Theoretical development and design of FIR filters, like frequency sampling filters, equalizers, inverse filters, optimal filters, smoothing filters. Spectral analysis and synthesis. Network structures for infinite impulse response (IIR) and FIR filters. Design of nonlinear filters, like ordered-statistics filters, median and homomorphic filters. Also included are filters using fuzzy logic. Matlab will be used throughout the course.

Fuzzy Logic. Theory and Applications
Prerequisites are DSP I and a knowledge of Matlab or equivalent. Fuzzy logic, an artificial intelligence language, is one of the fastest growing technologies in the world. Successful applications of fuzzy logic are adjunct to solving highly nonlinear system problems. This fuzzy logic course has been given as regular 3-credit graduate course at the Mayo Graduate School, Rochester, Minnesota. Fuzzy logic is entering medical disciplines like open-heart surgery and cancer detection. Several engineering problem solutions using fuzzy logic will be outlined. In most of these examples, the fuzzy logic solution was superior to the conventional approach.

Covered in the course are crisp and fuzzy sets with their relations. Membership functions, inference, and defuzzification. Fuzzy arithmetic and algebra problems. Fuzzy rule-based systems and nonlinear simulations. Fuzzy decision making, classification, and recognition. Applications of fuzzy logic to digital control, filters, image processing, medicine, etc. The use of simple Matlab functions, which are provided with the course.

Image Processing
Prerequisite DSP I and a knowledge of Matlab or equivalent. Two dimensional (2D) signals and systems, 2D discrete-time Fourier transforms (DTFT), 2D discrete Fourier transforms (DFT), 2D z-transforms, and the 2D discrete cosine transform (DCT). Design of 2D filters using frequency transformation, frequency sampling and windowing. Noise reduction methods. Design of Wiener and median filters. Image enhancements, like histogram equalization and homomorphic filtering. Morphological methods. Image compression techniques. Requires the use of Matlab or equivalent.

Digital Control Systems
After a quick review of digital signal processing concepts and transforms, the course enters into transfer function and state-space modeling of real-time physical systems with delay. The discretization of these models is done via the Zero-Order-Hold equivalence and the matched z-transforms. Analysis of stability of closed-loop control systems with various convenient performance criteria are discussed. The concepts of controllability and observability are covered. The designs of state observers or estimators (Predictor, Reduced-Order, Kalman) are discussed. Ample time is spent of the design of feedback controllers using both pole-placement techniques with Ackermann's formula and linear quadratic (LQ) techniques. State variable feedback and integral feedback are also discussed. Various disturbance reduction techniques will be highlighted. The software program Matlab is used throughout the course for the design and simulations in examples and homework.