Cosc 4242 Signals and Systems Introduction

Motivation Modeling, characterization, design and analysis of natural and man-made systems General approaches -> based upon theoretical and mathematical techniques Tools based upon the description and analysis of systems using differential and difference equations Time versus frequency domain representations – Fourier techniques

Applications Communications – AM, FM, FSK, PSK, communication channels Physical systems modeling and control- seismology, mechanics, chemical process control, aerospace, motor control, thermodynamics, fluid dynamics Radio-astronomy, geophysics Optics and acoustics

Applications Biomedical engineering Electronics, circuit design Neural networks, adaptive systems Computer vision, graphics, image and speech processing Time series analysis, economic forecasting, stock trends

Biomedical Applications - Heart Sounds

Audio Applications – Speaker Specifications

Financial Applications – Stock Trends Nortel from cnnfn.com

Radar Application- Focusing SAR images

Before processing

After focusing using array processing techniques

Aerospace Applications – Aircraft dynamics and control

Analogue versus Digital Signal Processing Main distinction is continuous versus discrete Analogue signal processing – many real world systems are analogue, control and processing in analogue domain with analogue circuits (RLC, diodes, amps....) or with mechanical or other physical elements DSP – digital circuits/program (adders, multipliers and memory)

Why Analogue? Natural solution of differential equations Strong arsenal of techniques for design of analogue filters etc. No need for approximation, sampling, numerical computations Real time, less complex circuitry BUT component values drift, imprecise tolerance, age and temperature variations, difficult with very small and very large components, non ideal realizations

Why Digital? Flexible, same hardware can perform multiple functions, upgrade and update possible Repeatability and precision, higher-order systems Natural for interface with high level supervisory control software BUT takes time to compute and circuit complexity is high (especially with general purpose hardware)

Most systems are ‘mixed’ combining some analogue and some digital components –digital hardware is so cheap it almost always an option despite increased circuit complexity for digital implementation Digital techniques for data acquisition, signal filtering, detection, processing and automatic control are sometimes approximations of analogue solutions and are sometimes fully ‘digital’ designs

Necessary/Useful Mathematical Preparation Calculus Linear algebra –Especially eigenvalue problem, orthogonality, basis functions Discrete math, sequences and series Numerical methods