Chapter 3 Problem solution Homework: 3.13.133.153.343.35
Chapter 3 Problem Solution Homework: 3.1 3.13 3.15 3.34 3.35
Chapter 3 Problem solution 3. 13 Consider a continuous-time lti system HGo sin(4a) 10<t<4 -14≤t<8 y()=∑aH(/koe=0 k=-00
Chapter 3 Problem Solution 3.13 Consider a continuous-time LTI system ( ) ( ) sin 4 H j = ( ) − = 1 4 t 8 1 0 t 4 x t ( ) ( ) 0 0 = 0 = =− j k t k k y t a H j k e
Chapter 3 Problem solution o≤100 315H(o) 0o>100 (),T=6-5>y()=x() For what values of k is guaranteed that ak =0? a4=0k}>8 1|o|≥250 3.35H(10)= x(),T=/7-S>y()=x() 0 otherwise For what values of k is guaranteed that ar=0? ak=0k<18
Chapter 3 Problem Solution 3.15 ( ) = 0 100 1 100 H j x(t) T = π/ ⎯→ y(t) = x(t) S , 6 For what values of k is guaranteed that = 0? ak 0 8 k a k = 3.35 ( ) = 0 otherwise 1 250 H j x(t) T = π/ ⎯→ y(t) = x(t) S , 7 For what values of k is guaranteed that = 0? ak 0 18 k a k =
Chapter 3 Problem solution 3.34 Consider a continuous-time LTI system h()=e41 Find the Fourier series representation of the output y(o) for each of the following inputs: (a)x()=∑6(t-n) (b)x()=∑(-yo(-n) n=-0 (c)x(t) is the periodic wave depicted in Figure P3. 34 2
Chapter 3 Problem Solution 3.34 Consider a continuous-time LTI system Find the Fourier series representation of the output for each of the following inputs : ( ) 4 t h t e − = y(t) x(t) (t n) n = − + =− (a) x(t) ( ) (t n) n n = − − + =− (b) 1 (c) is the periodic wave depicted in Figure P3.34 x(t) 1 x(t) -2 -1 0 1 2 t 1/ 2
Chapter 3 Problem solution cos @ot sin.t (o)y() cos OotH(joo)cos[o,t +AH (joo)J sin.t H(jOo)sin[Ont+AH(jOo)
Chapter 3 Problem Solution cos cos 0 0 0 0 ( ) ( ) L t H j t H j ⎯⎯→ + H j ( ) y t( ) 0 cos t 0 sin t sin sin 0 0 0 0 ( ) ( ) L t H j t H j ⎯⎯→ +
Chapter 3 Problem solution Consider an LTI system S with impulse response h(0) sin zt t Determine the output of S for the input x()=2x(t-3n) Suppose we are given x(= 1-1<I<1 10 others 2丌 y() 22n 132z + COS——t 3 3
( ) t t h t sin Consider an LTI system S with impulse response = Determine the output of S for the input Suppose we are given x(t) x (t n) n = 1 −3 + =− ( ) = 0 others 1 1 1 1 - t x t Chapter 3 Problem Solution y(t) t 3 2 cos 3 2 2sin 3 2 = +
