信号与系统北京交通大学考试题1

Mid-semester Testcourse：Signals & Systems, 2006.5 Name： class and number： score： 1（5 scores）1）Determine the Fourier Transform and for the signals and ;2) sketch 3)*advanced：determine energy of signal according to FT properties2. （6 scores） An interconnection of LTI systemsis depicted in following figure. if 1） Determine the impulse response of the overall system, and sketch ;2） Is this system a) stable? b) causal?;3） If input，sketch and the output;3. （5 scores）A continuous-time periodic signal 1） determine the FS coefficients ，sketch the magnitude and phase spectra;2） If pass a LTI system which has frequency response , determine and sketch its spectra.4. （7 scores） Determine the output of the systems described by following differential equation: ，1） Determine zero-initial response and zero-state response ;2） If ，reconsider 1);3） Draw direct form implementations for the system.4) Determine a state-variable description according to 3)5. （7 scores） A LTI discrete-time system is show as following,1） Find difference-equation descriptions for the system;2） Determine and sketch the impulse response ;3） If depicted as following, determine and sketch the output ;4） Determine the frequency response ，sketch the magnitude spectra, Is this system low-pass or high-pass?Answers:1.（1），（2） 211/213/2（3）E=10/p 2. （1）h(t)=u(t)-u(t-2) (2) stable, causal(3) t(1)4(1)-4(1)0(-1)-2(-1)2t4-40-221-13. （1），（2）y(t)=2+cos(pt), 4、(1),，（2），（4），,5、（1）y(n)=x(n)+ x(n-1) +x(n-2) （2）h(n)=d(