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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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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,
  • Advanced applications on signal processing:
    • Time frequency and wavelet
  • Detection and classification in signals
chapter 2 random functions
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
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
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
slide20

Jointly Stationary Properties

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