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Unformatted text preview: 6.450 Principles of Digital Communication Wednesday, October 9, 2002 MIT, Fall 2002 Handout #23 Due: Wednesday, October 16, 2002 Problem Set 6 Problem 6.1 (a) Show that for any T > 0 the set of functions { m,k ( t ) = e 2 imt/T sinc( t kT T ) } is an orthogonal set. Hint: Show that the Fourier transforms of each of these functions are orthogonal to each other; review the argument used for the T spaced truncated sinusoids. (b) Derive the energy equation, Eq. (13) in Lecture 9. Problem 6.2 The following exercise is designed to illustrate the sampling of an ap proximately baseband waveform. To avoid messy computation, we look at a waveform baseband limited to 3/2 which is sampled at rate 1 ( i.e. , sampled at only 1/3 the rate that it should be sampled at). In particular, let u ( t ) = sinc(3 t ). (a) Sketch u ( f ). Sketch the function v m ( f ) = rect( f m ) for each integer m such that v m ( f ) 6 = 0. Note that u ( f ) = m v m ( f )....
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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.
 Spring '08
 DanielLee

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