ps6 - 6.450 Principles of Digital Communication Wednesday,...

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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.

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ps6 - 6.450 Principles of Digital Communication Wednesday,...

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