Cosc 4242 Signals and Systems

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Cosc 4242 Signals and Systems

• Introduction

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Motivation

• Modeling, characterization, design and analysis
  of natural and man-made systems
• General approaches -gt 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

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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

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Applications

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

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Biomedical Applications - Heart Sounds
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Audio Applications Speaker Specifications
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Financial Applications Stock Trends
Nortel from cnnfn.com
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Radar Application- Focusing SAR images
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Before processing
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After focusing using array processing techniques
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Aerospace Applications Aircraft dynamics and
control
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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)

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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

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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)

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• 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

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Necessary/Useful Mathematical Preparation

• Calculus
• Linear algebra
• Especially eigenvalue problem, orthogonality,
  basis functions
• Discrete math, sequences and series
• Numerical methods