16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde atole 2xa'S(o)+oze jeeardr+dze-jore-irdr =2ra2o(m)+ (2-p)r =2na26()+σ n-j@ 2+ 2xa'5(o)+2004 S、(o) 20 Example: A signal random process Reference: Newton, G C, L.A. Gould and J F Kaiser. Design of linear Feedback Controls. John Wiley, 1961. P 100 Papoulis calls this the semirandom telegraph signal; p. 288 A signal takes the values plus and minus xo only. It switches from one leve to the other at " event points" which are Poisson distributed in time with constant average frequency a. This is sometimes called a telegraph signal16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 6 of 8 ( ) ( ) 2 2 0 22 2 0 0 2 2 2 0 2 2 2 2 2 2 ( ) 2 () 2 () 1 1 2 () 2 2 () j xx a j j a a a a j j a a S a e ed a e ed e e d ae e j j a j j a λ τ ωτ ωτ λτ ωτ λτ λ ωτ λ ωτ ωσ τ π δω σ τ σ τ σ σ π δω λω λω π δω σ λ ωλ ω σ λ π δω λ ω ∞ − − −∞ ∞ − −− −∞ ∞ − −+ −∞ = + ⎡ ⎤ ⎣ ⎦ =+ + =+ + − −− ⎡ ⎤ =+ + ⎢ ⎥ ⎣ ⎦ − + = + + ∫ ∫ ∫ Example: A signal random process Reference: Newton, G.C, L.A. Gould and J.F. Kaiser. Design of Linear Feedback Controls. John Wiley, 1961. p.100. Papoulis calls this the semirandom telegraph signal; p.288. A signal takes the values plus and minus 0 x only. It switches from one level to the other at “event points” which are Poisson distributed in time with constant average frequency λ . This is sometimes called a telegraph signal