信号与系统课堂练习

On class exercise1.The period of x[n]=cos(πn/8)+sin(2n) is , x(t)=cos(4πt)+sin(4t) is?2.The expression for x(t) illustrated in Figure 1 is ?3.consider a continuous-time system with input x(t) and output y(t) related by this system may be ( ).(a) Linear, time-variant,causal,stable(b) Linear, time-variant, not causal, unstable(c) Nonlinear, time-variant, causal, stable(d) Linear, time-variant, causal,unstatble4.Consider an LTI system with unit impulse response h(t) illustrated in Figure 2. if the input is x(t)=u(t),the ouput ( ) ?h(t) 0 t5.The convolution integral y(t)=[u(t)-u(t-1)]*[u(t-1)-u(t-3)] is( )(a) (t-1)u(t-1)+(t-2)u(t-2)-(t-3)u(t-3)-(t-4)u(t-4)(b) tu(t)-(t-1)u(t-1)-(t-2)u(t-2)+(t-3)u(t-3)(c) (t-1)u(t-1)-(t-2)u(t-2)-(t-3)u(t-3)+(t-4)u(t-4)(d) tu(t)+(t-1)u(t-1)-(t-2)u(t-2)-(t-3)u(t-3)6. (a) 1 (b) –1 (c) –0.5 (d) 0.57. Consider an LTI system whose input x[n] and unitimpulse response h[n] are given by x[n]={3,2,1},n=-1,0,1 h[n]={-1,2,3},n=0,1,2 The output y[n]=x[n]*h[n] is ?12-1 1 21-1 1 28.Consider a continuous-time system S whose frequency response is 1 , |ω|<=100π H(jω)=0, otherwise x(t)=∑ak e j6kπt, if the output y(t)=x(t), we can justify that for what values of k is it guaranteed that ak=0.9. Let x(t) be a periodic signal with fundamental frequency ω0 and Fourier series coefficients ak. The Fourier seies coefficients of x(1-t) is ?10. Consider a CT LTI system with impulse response if the input the FS representation of the output y(t) is( ).11. is ( )12. Consider an LTI system with unit impulse response if the input , the output y(t) is ( )13. Consider a CT LTI system with frequency response in the following figure. When the input is a periodic signal x(t) with fundamental period T=1 and FS coefficients , it is found y(t)=x(t), The input signal x(t) satisfy( ).(a) (b) =0, k=0 (c) (d) 14. The system: may be ( ) (a) Linear (b) TI (c) NC (d) Stable15. Consider a CT LTI system whose frequency response is . When the input is , it is found y(t)=0. Which of the following statements are true ( )(a) (b) (c) (d) -ππ116. We are given a certain LTI system with unit impulse response , and . Which of the following statements is FALSE( )(a) (b) (c ) (d)