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Advanced signal processing Dr. Mohamad KAHLIL Islamic University of Lebanon. Outline. Random variables Histogram, Mean, Variances, Moments, Correlation, types, multiple random variables Random functions Correlation, stationarity, spectral density estimation methods

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Presentation Transcript
slide1
Advanced signal processing

Dr. Mohamad KAHLIL

Islamic University of Lebanon

outline
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
chapter 4 detection and classification in random signals
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
slide4

Detection: definition

Hypotheses :

estimated

Known or unknown

gaussian distributions
Gaussian distributions

Normal distributions

slide6

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

fisher test
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

detection definition
Detection: definition

Hypotheses :

estimated

Known or unknown

parameters definition
Parameters definition
  • False alarm
    • Detect H1, H0 is correct
  • Detection
    • Detect H1, H1 is correct
  • Miss detection
    • Detect H0, H1 is correct
likelihood ratio
Likelihood ratio
  • Detection in signals
variation in mean
Variation in mean
  • Detection in mean

H0: z(t) = 0 + b(t) = b(t)

H1: z(t) = m + b(t)

detection in variance
Detection in variance
  • Detection in variance
parameters
Parameters
  • False Alarm probability
  • Detection probability
neymen pearson method
Neymen pearson method
  • Fix the probability of false alarm
  • Estimate the threshold