Assignment 1 soultion

Assignment 1 soultion - 1 ENSC-380, Spring 2009 Solutions...

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1 ENSC-380, Spring 2009 Solutions to Assignment 1 Chapter 2, Solution 30. Sketch these combinations of CT functions. (c) () () ( ) g4 r a m p u tt =− 2 t (h) ( )( ) gr e c t t r i = ( ) t (p) () ( ) ( ) ( ) g1 2 t td 1 δ λδλ λ −∞ ⎡⎤ =+ −+ ⎢⎥ ⎣⎦ (s) () () 4sinc 2 sgn t t Chapter 2, Solution 39. Using a change of variable and the definition of the unit impulse, prove that () ( ) 00 1 at t t t a δδ . ( ) 0, 0 xx = , 1 x dx −∞ =
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2 () ( ) 00 0,w h e r e 0o r at t t t δ ⎡⎤ −= −≠ ⎣⎦ 0 0 Strength d t −∞ =− Let ( ) 0 and a t t adt d λ ∴ = Then, for a > 0, 11 Strength d d aa δλ ∞∞ −∞ −∞ 1 = == ∫∫ = and for a < 0, 111 Strength d dd a aaa −∞ −∞ = = = ∫∫ ∫ 1 a Therefore for a > 0 and a < 0, 1 Strength a = and 1 t t a δδ . Chapter 2, Solution 48. Find the even and odd parts of each of these CT functions. (c) 2 x8 7 tt =+ ( ) 2 2 2 87 7 + 2 e ++ +− , 2 2 x0 2 o t −− = = (j) () ( ) ( ) 2 g8 7 s i n 3 2 tt t π ( ) () ( ) ( ) 2 2 87 s i n3 2 s i n 3 2 g0 2 e t t ππ + ( ) ) ( ) ( ) 2 2 2 i 2 s i 2 2 o t 7 s i n 3 2 t + + Chapter 2, Solution 51. For each of the following signals decide whether it is periodic and, if it is, find the period. (b) g t ()= 14 + 40cos 60 t Periodic. Fundamental frequency = 30 Hz Period =
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Assignment 1 soultion - 1 ENSC-380, Spring 2009 Solutions...

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