TU Wien:Verarbeitung Stochastischer Signale VU (Matz, Winkelbauer)/Oral exam 29.06.2015

Written exam: 49/70 Exercise points: 46/49

Random processes: ~15 minutes:

• Autocorrelation function of stationary processes
  • Definition
  • Properties (even, real for real processes, maximum at origin = mean power)
• PSD
  • Definition
  • Properties (periodic, non-negative, even & real for real processes)
  • Correspondence with autocorrelation (inverse fourier transform, power for m=0)
• Graph given - can this be a autocorrelation function? (No, had local/global minimum at origin)
• PSD of random processes filtered by LTI-system
  • How is the resulting process defined? (convultion of input process with impulse response)
  • How can we compute the PSD of the resulting process? (Sx * |H|^2 ... |H|^2 from fourier transform of convolution of impulse response)

Characteristic function/moment generation function ~15 minutes:

• Definion of both functions
• Relationship of char/mom.gen. function (set s=jw)
• Why do they characterize random variables compeletely? (moments as k-th derivative, moment occur in taylor-expansion)
• Applications? (Sum of independent random variables, chernoff inequality)
• Derivation of Chernoff inequality using Markov inequality and moment generating function

Result -> S1