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Simulation

Realizable Systems (Chap 22.4)

Causality and spectral factorization (Chap 22.4)

Simulating a w.s.s. Random Sequence (Chap. 15.4)

  1. 1212|lnSXf|df<
  2. G(f)=expa02+n=1anzn, where an=1212lnSXfei2πfndf, z=ei2πf
  3. Causal iff GZ(z) analytic on and outside unit circle.
  4. SX(f) is real, then SX(z) zeros/poles are in conjugate reciprocal pairs; SX(f) is nonnegative, then SX(z) zeros/poles are on unit circle and have even order; RX(0)<, then there are no poles on unit circle
  5. on unit circle, z1=z

Simulating a w.s.s. Random Waveform

  1. SX(f) is real, then zeros/poles are in conjugate pairs; SX(f) is nonnegative, then SX(z) zeros/poles have even order; RX(0)<, then there are no real poles.
  2. Causal iff H(f) analytic on and below real line.
  3. X(u,t) being real implies poles/zeros of SX(f) are symmetric about the origin.


🏷 Category=Probability