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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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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,
• Advanced applications on signal processing:
• Time frequency and wavelet
• Detection and classification in signals
Chapter 2: Random functions
• Definitions
• Probability density functions
• Cumulative density functions
• Moments of a random functions
• Covariance
• Stationary process
• Statistical auto and inter-correlation
• Spectral density estimation
• From autocorrelation
• Bank filters method
• Periodogram
• White noise analysis
Random functions
• Let us consider the random process : measure the temperature in a room
• Many measurements can be taken simultaneously using different sensors (same sensors, same environments…) and give different signals

z1

t

t1

t2

z2

Signals obtained when measuring temperature using many sensors

z3

PDF and CDF of Random Process
• Probability density function is fX(x;t) or f(x1,x2,x3,…xn;t1,t2,…tn)
• Cumulative density function
• We can write

Jointly Stationary Properties

• Properties
• Uncorrelated:
• Orthogonal:
• Independent: if x(t1) and y(t2) are independent (joint distribution is product of individual distributions)