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# Advanced signal processing Dr. Mohamad KAHLIL Islamic University of Lebanon - PowerPoint PPT Presentation

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

Islamic University of Lebanon

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
• Detection
• Definition
• Statistical tests for detection
• Likelihood ratio
• Example of detection when change in mean
• Example of detection when change in variances
• Multidimensional detection

Detection: definition

Hypotheses :

estimated

Known or unknown

Gaussian distributions

Normal distributions

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

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

Hypotheses :

estimated

Known or unknown

Parameters definition
• False alarm
• Detect H1, H0 is correct
• Detection
• Detect H1, H1 is correct
• Miss detection
• Detect H0, H1 is correct
Likelihood ratio
• Detection in signals
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
Parameters
• False Alarm probability
• Detection probability
Neymen pearson method
• Fix the probability of false alarm
• Estimate the threshold