Assignment 5 soultion

# Assignment 5 soultion - around 100Hz (see ﬁgure in the...

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School of Engineering Science Simon Fraser University ENSC-380, Spring 2009 Solution of Assignment 5 Solution of Problem 1. H ( f ) = 4 25 - 4 π 2 f 2 + j 12 πf e j 2 πf , h ( t ) = e - 3( t +1) sin(4( t + 1)) u ( t + 1) Not casual H ( f ) = 49 49+4 π 2 f 2 , h ( t ) = 49 14 e - 7 | t | Not casual H ( F ) = j sin(2 πF ), h ( n ) = 1 2 ( δ [ n + 1] - δn - 1) Not casual H ( F ) = 8 e j 2 πF 8 - 5 e - j 2 πF , h ( n ) = ( 5 8 ) n +1 u ( n + 1) Not casual Solution of Problem 2. H ( f ) = 1 1+ jf , | H ( f ) | = 1 1+ f 2 and Phase of H ( f ) = - atan( f ), Lowpass -100 -50 0 50 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Magnitude -100 -50 0 50 100 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Phase H ( f ) = jf 1+ jf , | H ( f ) | = 1 1+ f 2 and Phase of H ( f ) = π 2 - atan( f ), Lowpass 1

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-100 -50 0 50 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Magnitude -100 -50 0 50 100 0 0.5 1 1.5 2 2.5 3 3.5 Phase Solution of Problem 3. We have: G ( f ) = 1 2 j ( M ( f - 50) - M ( f + 50)) and let x ( t ) be the input to the LPF: x ( t ) = g ( t )cos(100 πt ) therefore X ( f ) = 1 2 ( G ( f - 50) + G ( f + 50)) Replacing G ( f ): X ( f ) = 1 2 ( 1 2 j ( M ( f - 100) - M ( f )) + 1 2 j ( M ( f ) - M ( f + 100))) = 1 4 j ( M ( f - 100) - M ( f + 100)) The LPF has a bandwidth of 10Hz while the input to it (i.e., x ( t )) has a bandwidth of 10Hz

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Unformatted text preview: around 100Hz (see ﬁgure in the next page). Therefore, the LPF will have an output of zero: y ( t ) = 0. 2 3 School of Engineering Science Simon Fraser University ENSC-380, Spring 2009 Solution to Assignment 5, Problem 2, Part 2 Problem 2. Draw the phase and magnitude of the following ﬁlters and classify them (lowpass, highpass, or bandpass): • Part 2 H ( f ) = jf 1+ jf | H ( f ) | = | f | p 1 + f 2 ∠ H ( f ) = π 2 + | f | f π-tan-1 ( f ) = | f | f π 2-tan-1 ( f )-10-8-6-4-2 2 4 6 8 10 0.2 0.4 0.6 0.8 1 Magnitude of H(f)=jf /1+jf f |H(f)|-10-8-6-4-2 2 4 6 8 10-2-1.5-1-0.5 0.5 1 1.5 2 f Phase (rad) Phase of H(f)=j f /(1+jf) 1...
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## This note was uploaded on 04/12/2011 for the course ENSC 380 taught by Professor Atousa during the Spring '09 term at Simon Fraser.

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Assignment 5 soultion - around 100Hz (see ﬁgure in the...

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