Electrical Engineering 20N - Fall 1999 - Midterm 2

Electrical Engineering 20N - Fall 1999 - Midterm 2 - EECS...

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EECS 20. Solutions to Midterm No. 2. November 12, 1999. 1. 20 points Let x : Reals Comps be a continuous-time signal with Fourier Trans- form X .T h e bandwidth of x is de±ned to be the smallest number Ω x (rads/sec) such that | X ( ω ) | =0for | ω | > x . If there is no such ±nite number, Ω x = . Answer the following and give a brief justi±cation for your answer. (a) If t,x ( t ) = 1, what is X and what is the bandwidth of x ? ω,X ( ω )=2 πδ ( ω ), and so Ω x =0 . (b) If t,x ( t )= δ ( t ) (Dirac delta), what is X and what is the bandwidth of x ? ω,X ( ω ) = 1, and so Ω x = . (c) If t,x ( t )=cos( t ), what is X and what is the bandwidth of x ? ω,X ( ω )= π [ δ ( ω 1) + δ ( ω +1)],andsoΩ x =1 . (d) If x has bandwidth Ω x what is the bandwidth of the signal 2 x ? Since the Fourier Transform of 2 x is 2 X ,Ω 2 x
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This note was uploaded on 05/17/2009 for the course EE 20N taught by Professor Ayazifar during the Spring '08 term at Berkeley.

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Electrical Engineering 20N - Fall 1999 - Midterm 2 - EECS...

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