# ps8-PAM - 6.450 Principles of Digital Communication MIT,...

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6.450 Principles of Digital Communication Wednesday, October 30, 2002 MIT, Fall 2002 Handout #29 Due: Wednesday, November 6, 2002 Problem Set 8 Problem 8.1 Given two waveforms u 1 , u 2 ∈ L 2 let V be the set of all waveforms v that are equi-distant from u 1 and u 2 . Thus V = n v : k v - u 1 k = k v - u 2 k o . (a) Is V a vector sub-space of L 2 ? (b) Show that V = n v : h v , u 2 - u 1 i = k u 2 k 2 - k u 1 k 2 2 o . (c) Show that ( u 1 + u 2 ) / 2 ∈ V (d) Give a geometric interpretation for V . Problem 8.2 Expand the function sinc(3 t/ 2) as an orthonormal expansion in the set of functions { sinc( t - n ) } ; -∞ < n < ∞} . Problem 8.3 Consider M -PAM where the M signals are A = {- d ( M - 1) / 2 ,... , - d/ 2 ,d/ 2 ,...d ( M - 1) / 2 } Assume that the signals are used with equal probability. Show that the average energy per symbol E s = A 2 is equal to the average energy U 2 = d 2 M 2 / 12 of a uniform continuous distribution over the interval [ - dM/ 2 ,dM/ 2], minus the average energy

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## This note was uploaded on 10/07/2009 for the course ENSC 5210 taught by Professor Daniellee during the Spring '08 term at Simon Fraser.

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ps8-PAM - 6.450 Principles of Digital Communication MIT,...

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