hw3sol

hw3sol - Instructor: Christopher Wayne Walker, Ph.D. TA:...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Instructor: Christopher Wayne Walker, Ph.D. TA: Federico Cattivelli EE132A Winter 2008 EE 132A Homework 3 Solutions Problem 1. Proakis & Salehi 2.16 parts 2 and 13. Solution: 2) Nolinear, if we multiply the input by a constant -1, the output does not change. In a linear system the output should be scaled by -1. 13) Linear, we can write the output of this feedback system as y ( t ) = x ( t ) + y ( t − 1) = ∞ summationdisplay n =0 x ( t − n ) Then for x ( t ) = αx 1 ( t ) = βx 2 ( t ) y ( t ) = ∞ summationdisplay n =0 [ αx 1 ( t − n ) + βx 2 ( t − n )] = α ∞ summationdisplay n =0 x 1 ( t − n ) + β ∞ summationdisplay n =0 x 2 ( t − n ) = αy 1 ( t ) + βy 2 ( t ) Problem 2. Proakis & Salehi 2.24 parts 1 and 9. Solution: 1) The invariant: The response to x ( t − t ) is 2 x ( t − t ) + 3 which is y ( t − t ). 9) Time-invariant system. Writing y ( t ) as ∑ ∞ n =0 x ( t − n ) we get y ( t − t ) = ∞ summationdisplay n =0 x ( t − t − n ) = T [ x ( t − t )] Problem 3. Proakis & Salehi 5.6. Solution: 1) X can take four different values: 0 if no head shows up, 1 if only one head shows up in the four flips of the coin, 2 for two heads, and 3 if the outcome of each flip is head. 2) X follows the binomial distribution with n = 3. Thus P ( X = k ) = parenleftbigg 3 k parenrightbigg p k (1 − p ) 3- k for 0 ≤ k ≤ 3 otherwise 3) F X ( k ) = k summationdisplay m =0 parenleftbigg 3 m parenrightbigg p m (1 − p ) 3- m 1 Instructor: Christopher Wayne Walker, Ph.D. TA: Federico Cattivelli EE132A Winter 2008 Hence F X ( k ) = k < (1 − p ) 3 k = 0 (1 − p ) 3 + 3 p (1 − p ) 2 k = 1 (1 − p ) 3 + 3 p (1 − p ) 2 + 3 p 2 (1 − p ) k = 2 (1 − p ) 3 + 3 p (1 − p ) 2 + 3 p 2 (1 − p ) + p 3 = 1 k = 3 1 k > 3 A plot of F X ( k ) is shown in Figure 1.) is shown in Figure 1....
View Full Document

This note was uploaded on 03/18/2008 for the course EE 132A taught by Professor Walker during the Winter '08 term at UCLA.

Page1 / 5

hw3sol - Instructor: Christopher Wayne Walker, Ph.D. TA:...

This preview shows document pages 1 - 3. Sign up to view the full document.

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