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Advanced Signal Processing: Detection & Classification in Random Signals

Learn statistical tests, likelihood ratio, and applications in signal processing. Understand detection for changes in mean and variance, hypothesis testing with Gaussian distributions, and multidimensional cases.

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Advanced Signal Processing: Detection & Classification in Random Signals

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  1. Advanced signal processing Dr. Mohamad KAHLIL Islamic University of Lebanon

  2. Outline • Random variables • Histogram, Mean, Variances, Moments, Correlation, types, multiple random variables • Random functions • Correlation, stationarity, spectral density estimation methods • Signal modeling: AR, MA, ARMA, • Detection and classification in signals • Advanced applications on signal processing: • Time frequency and wavelet

  3. Chapter 4: detection and classification in random signals • Detection • Definition • Statistical tests for detection • Likelihood ratio • Example of detection when change in mean • Example of detection when change in variances • Multidimensional detection

  4. Detection: definition Hypotheses : estimated Known or unknown

  5. Gaussian distributions Normal distributions

  6. Chi2 distributions Loi du Chi 2 (Khi-two of Pearson) 10 dof 15 dof  chi2 with k degree of freedom E[chi2]=k Variance of Chi2=2k

  7. Fisher Test Student distribution F(6,7) F(6,10) Student with k degree of freedom Fisher-Snédécor Distribution Fisher with k and l degree of freedom Example: Detection in signals

  8. Detection: definition Hypotheses : estimated Known or unknown

  9. Parameters definition • False alarm • Detect H1, H0 is correct • Detection • Detect H1, H1 is correct • Miss detection • Detect H0, H1 is correct

  10. Likelihood ratio • Detection in signals

  11. Variation in mean • Detection in mean H0: z(t) = 0 + b(t) = b(t) H1: z(t) = m + b(t)

  12. Detection in variance • Detection in variance

  13. Parameters • False Alarm probability • Detection probability

  14. Parameters

  15. Neymen pearson method • Fix the probability of false alarm • Estimate the threshold

  16. Detection: multidimensional case • Multidimensional case

  17. Distribution de Fisher-Snedecora = 0,05

  18. DISTRIBUTION DU KHI-DEUX

  19. DISTRIBUTION DU KHI-DEUX (suite)

  20. LOI NORMALE CENTRÉE RÉDUITE

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