SIGNAL AND SYSTEM CT Fourier Transform. Fourier’s Derivation of the CT Fourier...

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Transcript of SIGNAL AND SYSTEM CT Fourier Transform. Fourier’s Derivation of the CT Fourier...

  • Slide 1
  • SIGNAL AND SYSTEM CT Fourier Transform
  • Slide 2
  • Fouriers Derivation of the CT Fourier Transform x(t) -an aperiodic signal -view it as the limit of a periodic signal as T For a periodic signal, the harmonic components are spaced 0= 2/T apart... As T , 00, and harmonic components are spaced closer and closer in frequency Fourier series Fourier integral
  • Slide 3
  • Motivating Example: Square wave
  • Slide 4
  • Derivation
  • Slide 5
  • Derivation(continued)
  • Slide 6
  • Slide 7
  • For what kind of signals we do this
  • Slide 8
  • Example
  • Slide 9
  • CT Fourier Transforms of Periodic Signals
  • Slide 10
  • Example
  • Slide 11
  • Properties
  • Slide 12
  • Properties(continued)
  • Slide 13
  • Slide 14
  • 5.Differentiation and Integration 6.Duality
  • Slide 15
  • Properties(continued) 7.Parsevals Relation 8.Multiplication Property 9.Convolution Property
  • Slide 16
  • LTI System characterized by Differential Equations (Some slides are referred from MIT )