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Signals and systems: an Introduction to Analog and Digital Signal Processing

Lecture 1: Introduction

• Signals
  • continuous time
    • speech signal
      • $\mathrm{x}(t)$ one dimensional
    • images
      • $\mathrm{brightness(horiz, vert)}$ two dimensional
    • for convenience, we tend to refer to the independent variables when we talk about signals as time variables. Whether or not they really do represent time.
  • discrete time
    • stock market index
    • $\mathrm{x[n]}$ one dimensional
    • spatial and time ray
      • $\mathrm{x[n,m]}$ multi-dimensional

• Systems
  • classification
    • linear or not
      • linear
      • Nonlinear
    • time-varying or not
      • time-invariant
      • time-varying
  • This course will focus on LTI - linear time-invariant systems
  • Interconnections of systems
    • series
    • parallel
    • feedback
  • Domains for analysis and representation
    • Time domain - How to change?
      • $\mathrm{x[n]}$
      • $\mathrm{x(t)}$
    • Frequency domain - How to represent?
      • Fourier transform
      • Laplace transform (Extensions of the Fourier transform)
      • z-transform (a discrete time counterpart of Laplace transform)