Question

The questions are about Fundamentals of Communication Systems, and Random variables and probability.

Please answer for the below one problem.

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Problem 3 Find the output autocorrelation function for a delay line with delay A when the input is a stationary process with the autocorrelation RX(T). Interpret the result.

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Answer 1

delay line : - In Analog delay line is a Network of electrical components connected in conscade & each element creats the required delay hlt) - Delay Line E ED of & impulse Response 'A amout of delay delay line for be defined com h(t) slt-A A) 1 hlt) At How ) slt) 1 A بال - slt-A e Hence Tremsfer function -JWA Hew) 2 csso Scanned with CamScanner

tet ginen input auto correlation fxh Rx (2) we know that Fourier Trems form of Auto corselention function is ef gives the Power spectral density hlt) Rx (1) HIS Sylf) Solf) H() w Ryle) line Ry (1) Sylf) Auto corselection for of delay PSD of F.T. of Ry (T) T Sylt) e luy sely we know the Relent of input & output PSD. Regent Sylf) | H(jw) 12: Sylf) -jwa :: [84-1 Sylf) Sx (f) Ang Rx (2) Ry(t) Hence output auto oselection fx of delay line =Rx(+) some as input autocosselent Wh Hence Scanned with CamScanner