assignment11 - R X ( ) = (1- | | /T ) or | | < T...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Assignment 11 1. (a) Find the autocorrelation function corresponding to the power spectral density shown in the following ±gure. (b) Find the total average power. (c) Plot the power in the range | f | > f 0 as a function of f 0 > 0. f - f 2 - f 1 0 f 1 f 2 A A B 2. Show that (a) R X,Y ( τ ) = R Y,X ( - τ ). (b) S X,Y ( f ) = S * Y,X ( f ). 3. Let R X ( k ) = 4( α ) | k | + 16( β ) | k | , α < 1, β < 1. (a) Find S X ( f ). (b) Plot S X ( f ) for α = β = 0 . 5 and α = 0 . 75 = 3 β and comment on the e²ect of value of α/β . 4. Let D n = X n - X n - d , where d is an integer constant and X n is a zero-mean, WSS random process. (a) Find R D ( k ) and S D ( f ) in terms of R X ( k ) and S X ( f ). What is the impact of d ? (b) Find E [ D 2 n ]. 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5. Let X ( t ) be a diferentiable WSS random process, and deFne Y ( t ) = d dt X ( t ) ±ind an expression ²or S Y ( f ) and R Y ( τ ). Hint : ±or this system, H ( f ) = j 2 πf . 6. Let Y ( t ) be a short-term integration o² X ( t ): Y ( t ) = 1 T i t t - T X ( t p ) dt p . (a) ±ind the impulse response h ( t ) and the trans²er ²unction H ( f ). (b) ±ind S Y ( f ) in terms o² S X ( f ). 7. In problem 6, Let
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: R X ( ) = (1- | | /T ) or | | &lt; T and zero elsewhere. (a) ind S Y ( f ). (b) ind R Y ( ). (c) ind E [ Y 2 ( t )]. 8. The input into a Flter is zero-mean white noise with noise power density N / 2. The Flter has transer unction H ( f ) = 1 1 + j 2 f (a) ind S Y,X ( f ) and R Y,X ( ) . (b) ind S Y ( f ) and R Y ( ). (c) What is the average power o the output? 9. (a) A WSS Gaussian random process X ( t ) is applied to two linear systems as shown in the ollowing Fgure. ind an expression or the joint pd o Y ( t 1 ) and W ( t 2 ). (b) Evaluate part a i X ( t ) is white Gaussian noise. h 1 ( t ) h 2 ( t ) X ( t ) Y ( t ) W ( t ) 2...
View Full Document

Page1 / 2

assignment11 - R X ( ) = (1- | | /T ) or | | &amp;amp;lt; T...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online