Chapter l Problems solution 作业:1.141.151.161.1 1.2l(d)(e)(f) 1.22(d)(g) 1.23 1.24(a)(b) 1.26(a)(b) 1.271.31
Chapter 1 Problems Solution 作业： 1.14 1.15 1.16 1.17 1.21 (d) (e) (f) 1.22 (d) (g) 1.23 1.24 (a) (b) 1.26 (a) (b) 1.27 1.31
Chapter l Problems solution 1.16 renin (a no, it is a system with memory. (b)xn]=An p四]}=A2δm] 2|=0 (c)Is this system invertible? N x四=A6Sn-1] pl以]=A2{n-l]5n-3]=0
Chapter 1 Problems Solution 1.16 yn= xnxn−2 (a) No ,it is a system with memory. (b) xn= A n 2 0 2 y n = A n n− = (c) Is this system invertible? No. xn= A n−1 1 3 0 2 y n = A n− n− =
Chapter 1 Problems solution 117y()=x(sin(t) (a) Is this system causal? (b) Is this system linear? (a) No y(-x)=x(sin(-z)=x(0) (b) Yes
Chapter 1 Problems Solution 1.17 y(t) = x(sin(t)) (a) No. y(− )= x(sin(− ))= x(0) (b) Yes. (a) Is this system causal? (b) Is this system linear?
Chapter 1 Problems solution 1. 27 A system may or may not be (1)Memoryless (2) Time invariant (3)Linear (4)Causal (5)Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems. a)y()=x(-2)+x(2-t) Linear, Time-varying, with memory, not causal, stable (b)y()=(cos 3t)x() Linear, Time-varying, memoryless, causal, stable ()y()= Linear, Time-varying, with memory, not causal, not stable
Chapter 1 Problems Solution 1.27 A system may or may not be (1) Memoryless (2) Time invariant (3) Linear (4) Causal (5) Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems. (a). y(t)= x(t −2)+ x(2−t) Linear , Time-varying , with memory , not causal , stable (b) y(t) = (cos3t)x(t) Linear , Time-varying , memoryless , causal , stable ( ) y(t) x( )d t − = 2 c Linear , Time-varying , with memory , not causal , not stable
Chapter 1 Problems solution 0 t<0 (a)y(t) x()+x(-2)t≥0 Linear, Time-varying, with memory, Causal, stable (e)y() 0 r(t)<0 x()+x(t-2)x()≥0 Nonlinear, Time-invariant, with memory, Causal, stable 〔)y()=x(/3) Linear, Time-varying, with memory, not causal, Stable g)J Linear, Time-invariant, with memory, causal, not stable
Chapter 1 Problems Solution ( ) ( ) ( ) ( ) + − = 2 t 0 0 , t 0 d x t x t y t Linear , Time-varying , with memory , Causal , Stable ( ) ( ) ( ) ( ) ( ) ( ) + − = 2 0 0 , 0 e x t x t x t x t y t Nonlinear , Time-invariant , with memory , Causal , Stable (f) y(t) = x(t / 3) Linear , Time-varying , with memory , not causal , Stable ( ) ( ) ( ) dt dx t g y t = Linear , Time-invariant , with memory , causal , not stable
Chapter l Problems solution 1.31 Consider an LTi system: al)x1()→y1() Determine and sketch x()→>y()=? (b) Determine and sketch the response of the system considered in part of (a) to the input x3(t). y() 012 012 x2() x3(t)2 234 10
Chapter 1 Problems Solution 1.31 Consider an LTI system: ( ) x (t) y (t) 1 1 a → Determine and sketch ( ) ( ) ? x2 t → y2 t = (b) Determine and sketch the response of the system considered in part of (a) to the input x3 (t). 0 1 2 1 x (t) 1 t 2 0 1 2 1 y (t) 1 t 3 4 −1 0 1 2 1 x (t) 2 t 2 −1 0 1 2 1 x (t) 3 t
Chapter l Problems solution y2 1.x2()=x1()-x(t-2) 2 y2(t)=y(t)-y1(-2) J1(t-2) 0123/4t 2.x3(t)=x1(t)+x1(+1) 2 (t)=y(t)+y1(+1) 2() y y1(+1) 2 2
Chapter 1 Problems Solution 1. ( ) ( ) ( 2) x2 t = x1 t − x1 t − ( ) ( ) ( 2) y2 t = y1 t − y1 t − 0 1 2 3 4 t 2 1 y (t) 2 − 2 2. ( ) ( ) ( 1) x3 t = x1 t + x1 t + ( ) ( ) ( 1) y3 t = y1 t + y1 t + 2 0 1 2 1 y (t) 1 t ( 1) y1 t + 2 0 1 2 1 y (t) 3 −1 t