Math 4392     SIGNALS AND SYSTEMS

Spring 2000     MWF   11:00 - 11:50

Instructor:  Dr. Seppo Seikkala

Department of Mathematics, University of Texas at Arlington


Contents:

1. INTRODUCTION

1.1. Classification of Signals
1.2. Time Domain Analysis of Signals
1.3. Frequency

2. FOURIER-ANALYSIS OF SIGNALS

2.0. Orthogonal Expansions, Wavelets
2.1. Periodic Analog Signal (Fourier Series)
2.2. Non-Periodic Analog Signal (Fourier Integral Transform)
        2.2.1. Definition, Amplitude Spectrum
        2.2.2. Properties of the Fourier Transform, Fourier Transform of a Convolution
        2.2.3. Dirac's Delta Function, Sampling Theorem
        2.2.4. Discrete Fourier transform and FFT, Frequency Resolution
2.3.* Periodic Discrete Signal
2.4. Non-Periodic Discrete Signal (Fourier Sum Transform)
2.5.* Windowing and Extrapolation

3. LINEAR TIME INVARIANT SYSTEM (LTI SYSTEM)

3.1. Analog System
3.2. Discrete LTI System
3.3. Compound Systems

4. ANALOG LTI SYSTEM

4.1. Transfer Function, Amplitude Response, Phase Response
4.2. Stability
4.3. Distortionless Transfer
4.4. Low Pass, High Pass, Band Pass, Band Stop Filter
4.5. Hilbert Transform
4.6. Amplitude Modulation
4.7. Angle Modulation, FM Modulation, PM Modulation
4.8. Analog Band Pass Signal, Sampling
4.9. Analog Signal, Reconstruction from Samples, D/A Converter
        4.9.1. Zero Order Hold
        4.9.2. First Order Hold
        4.9.3. Linear Interpolation with Delay
        4.9.4. Time Division Multiplexing, Frequency Division Multiplexing
4.10.* Digital Simulation of an Analog System

5. DISCRETE LTI SYSTEM

5.1 Frequency, Amplitude, and Phase Response, Stability
5.2. Distortionless Transfer, Linear Phase FIR Filter
5.3. Low Pass Filter -> High Pass Filter
5.4. Design of a Digital Filter by Placing Zeros and Poles
5.5. System Identification, Inverse System
        5.5.1. Inverse System
        5.5.2. System Identification and Deconvolution
        5.5.3. System Identification and the Method of Least Squares
5.6.* Design of IIR Filters by Analog Filters
        5.6.1. The Method of Approximation of Derivatives
        5.6.2. Impulse Invariance Method
        5.6.3. Bilinear Transformation Method

6.* STATE-SPACE ANALYSIS


Front page
Index
Notations
Tables
Problems