Samp Ta2009.Pptx

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Samp Ta2009.Pptx

  1. 1. 21st May 2009 – Marseille, France
  2. 2. Signal in time 2 Real part 1 0 -1 -2 Linear scale Energy spectral density 2000 1000 1500 500
  3. 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. 4. Signal of Interest Kernel
  5. 5. Eigen Functions Normalized Hermite Polynomials Eigen Values
  6. 6. ⎧ ⎫ ⎨ ⎬ FT · · · FT {Ψn (t)} = Ψn (t), ejωt = λp Ψn (ω) n ⎩ ⎭ p−times Possible because Eigen-functions are Orthonormal!
  7. 7. Sampling Kernel
  8. 8. 2 −j t2 cot θ ϕn (t) = e sinc(t − nT )

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