Chapter 2 Problems solution ,0≤n≤9 1.0≤n≤N 2.5 0. elsewhere 0. elsewhere =x小]*y4]=5,y4=0 Determine the value of n N=4
1 Chapter 2 Problems Solution N = 4 2.5 = 0, elsewhere 1, 0 n 9 x n = 0, elsewhere 1, 0 n N h n yn= xnhn y4= 5 , y14= 0 Determine the value of N
Chapter 2 Problems solution 2.7 A linear system S has the relationship =∑ xkgn-2 between its input xn] and output[n] gn]=un]-un-4 (a)x[小]=o[n-1]y[小=[n-21-u[n-6 (b)x{]=o8[n-2]y[小=utn-4]-m-8 (c)s is time-varying. uIn+uln =2u 6n-6n
2 Chapter 2 Problems Solution 2.7 A linear system S has the relationship yn xkgn k k = − 2 + =− between its input and output xn yn gn= un−un−4 (a 1 ) x n n = − y n u n u n = − − − 2 6 (b 2 ) x n n = − y n u n u n = − − − 4 8 (c) S is time-varying. (d ) x n u n = y n u n u n = + − 2 = − − − 2 1 u n n n
Chapter 2 Problems solution M0)=0(),0s161.0x1≤1 2.10 Suppose that 0 elsewhere (a)Determine y()=x(t)*h(t) (b)If dy(t/ dt contains only three discontinuities what is the value of a? Solution o a1 l+ t
3 Chapter 2 Problems Solution 2.10 Suppose that ( ) = 0, elsewhere 1, 0 t 1 x t h(t) = x(t / a) , 0 a 1 y(t) = x(t)h(t) d y(t) dt (a) Determine (b) If contains only three discontinuities,what is the value of a? Solution ： y(t) a 0 a 1 1+a t
Chapter 2 Problems solution 212Lety()=e"l()*∑o(-3k) k=-00 Show that y()=Ae' for 0<t<3 Determine the value ofa y()=c2=,1e 0≤t<3 e 4
4 Chapter 2 Problems Solution 2.12 Let ( ) ( ) ( ) =− − = − k t y t e u t t 3k Show that for ( ) t y t Ae− = 0 t 3 Determine the value of A. ( ) 3 3 0 1 0 t 3 1 t k t k y t e e e e + − − − − = = = − 3 1 1 A e − = −
Chapter 2 Problems solution 22(c) ( h() 2 one period of sin ru 米 0 123t 0 2 t 0 t<1 (1+cos t) l≤t≤3 y(t)= 1+ cos t)3≤t≤5 0 t>5 5
5 Chapter 2 Problems Solution 0 1 2 2 3 x(t) t sin t h(t) 0 1 2 1 t 2.22(c) one period of ( ) ( ) ( ) 0 t 1 2 1 cos 1 t 3 2 - 1 cos 3 t 5 0 t 5 t y t t + = +