ECE633F09_HW5solutions

ECE633F09_HW5solutions - ECE633 Signals and Systems I, Fall...

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ECE633 Signals and Systems I, Fall 2009 – Homework 5 Solutions 1 From: Linear Systems and Signals, 2 nd ed . B. P. Lathi, Oxford University Press, 2005. 2.4-7 The unit impulse response of an LTIC system is ( ) ( ) t ht eut = . Find this system’s (zero- state) response () yt if the input ( ) x t is: (a) ut (c) ( ) 2 t eu t (b) t (d) ( ) ( ) sin 3 tut Use the convolution table (Table 2.1) to find your answers. (a) () () () 1 1 t t e eut ut =∗ = −− ( )( ) 1 t e ut ⎡⎤ =− ⎣⎦ (b) tt eut eut ( ) t t = (c) ()() 2 2 12 ee eut e ut = −−− ( ) ( ) 2 e e (d) () () ( ) () () 33 sin 3 2 jt j ⎢⎥ () () () () ()( ) 11 22 1 3 1 3 tj t t j t t t j t eut e ut eut e ut jj j j = ( )( ) 13 1 21 3 1 3 t t j t je e e j −+ = 32 1 0 t j e y tu t j + = 1 10 2 2 t e j =+ () ( ) 3 sin 3 cos 3 10 10 10 t t e t ut OR
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ECE633 Signals and Systems I, Fall 2009 – Homework 5 Solutions 2 () () ( ) () ( ) ( ) ( ) 0 sin 3 cos 3 90 tt t yt eut tut eut e t ut −− =∗ ° () 10 1 2 2 33 cos 90 tan cos 3 90 tan 01 3 ee t yt ⎛⎞ ⎜⎟ −° +− ⎝⎠ = + ( ) ( ) 11 cos 90 tan 3 / 1 cos 3 90 tan 3 / 1 10 t et ° ° = ( ) ( ) 3/ 10 cos 3 18.43 cos tan 1/ 3 cos 3 tan 1/ 3 10 10 t t −+ ° =≈ () ( ) () cos 3 18.43 3 0.3 0.3162cos 3 18.43 10 10 t e e t ⎡⎤ ≈− + ° ⎢⎥ ⎣⎦ 2.4-11 Repeat problem 2.4-7 for ( ) ( ) t ht eut = and each of the following inputs x t : (a) 2 t eu t (b) ( ) 23 t t (c) 2 3 t t (d) The gate pulse depicted in Fig. P2.4-11 – and provide a sketch of . (a) () () () ()() 2 2 12 eut e ut = −−− ( )( ) 2 e e =− (b) () () 2 62 6 t t yt eut e ut eut ee ut e = ( ) ( ) e e e
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ECE633 Signals and Systems I, Fall 2009 – Homework 5 Solutions 3 (c) () () ( ) () () ( ) ( ) ()() 32 3 23 26 6 333 12 tt t t ee yt eut e ut eut ee ut e −− − − =∗− =∗ = −−− 3 6 3 yt e e e ⎡⎤ =− ⎣⎦ (d) () () () ( ) ( ) 1 11 t t t eut ut ut = () () 1 1 t t e ut e
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ECE633 Signals and Systems I, Fall 2009 – Homework 5 Solutions 4 2.4-18 Find and sketch () () ( ) 12 ct
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This note was uploaded on 02/11/2010 for the course ECE 633 taught by Professor Staff during the Fall '09 term at University of Texas.

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ECE633F09_HW5solutions - ECE633 Signals and Systems I, Fall...

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