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