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Samp Ta2009.Pptx

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Transcript

  • 1. 21st May 2009 – Marseille, France
  • 2. Signal in time 2 Real part 1 0 -1 -2 Linear scale Energy spectral density 2000 1000 1500 500
  • 3. Time-Frequency Representation of Signal of Interest (GMSK): Piecewise Polynomial Representation Gradient Operation at Level 1 Gradient Operation at Level 2 – The Piecewise Polynomial is Decomposed as a Impulse Functions Question: Assuming that this sequence of impulses can be transmitted and received with high fidelity, is this characterization good enough to model GMSK based communication system?
  • 4. Signal of Interest Kernel
  • 5. Eigen Functions Normalized Hermite Polynomials Eigen Values
  • 6. ⎧ ⎫ ⎨ ⎬ FT · · · FT {Ψn (t)} = Ψn (t), ejωt = λp Ψn (ω) n ⎩ ⎭ p−times Possible because Eigen-functions are Orthonormal!
  • 7. Sampling Kernel
  • 8. 2 −j t2 cot θ ϕn (t) = e sinc(t − nT )