Bài giảng Signal & Systems - Chapter 1: Elementary of signal and system

Nội dung text: Bài giảng Signal & Systems - Chapter 1: Elementary of signal and system

1. Ch-1: Elementary of signal and system P1.1 . A continuous-time signal f(t) shown in Figure P1.1. Sketch an label carefully each of the following signals: (a) f(t− 1) (b) f(2-t) (c) f(2t+1) t 3 3 (d) f(4− 2 ) (e) [f(t)+f(-t)]u(t) (f) f(t)[δ (t+2 )- δ (t− 2 )] Signal & Systems - FEEE, HCMUT – Semester: 02/10-11 Ch-1: Elementary of signal and system P1.2 . The continuous-time signal f(t) depicted in Figure P1.2. Sketch an label carefully each of the following signals: t t (a) f(t+3) (b) f(2 − 2) (c) f(1− 2t) (d) 4f(4 ) 1 t (e) 2 f(t)u(t)+f(− t)u(t) (f) f(2 )δ (t+1) (g) f(t)[u(t+1)− u(t − 1)] Signal & Systems - FEEE, HCMUT – Semester: 02/10-11 1
2. Ch-1: Elementary of signal and system P1.5 . (a) Find the energies of the pair signals x(t) and y(t) illustrated in Figure P1.5a and b. Sketch and find the energies of signals x(t)+y(t) and x(t)-y(t)? Can you make any conclusion from these results? (b) Repeat part (a) for signal pair illustrated in Figure P1.5c? Is the conclusion in part (a) still valid? Can you generalize condition of x(t) and y(t) that conclusion in part (a) always right? Signal & Systems - FEEE, HCMUT – Semester: 02/10-11 Ch-1: Elementary of signal and system P1.6 . Determine power of the following signals: f1(t)=C 1cos( ω1t+ θ1), f 2(t)=C 2cos( ω2t+ θ2), and f 1(t)+f 2(t) in two cases: (a) ω2=ω2, and (b) ω1≠ω2? P1.7 . Consider signal f(t) depicted in Figure P1.7. Find power of the following signals: f(t), -f(t), and 2f(t)? Signal & Systems - FEEE, HCMUT – Semester: 02/10-11 3
3. Ch-1: Elementary of signal and system P1.11 . Determine the even and odd parts of the following signals: (a) u(t); (b) tu(t); (c) sin( ω0t)u(t); (d) cos( ω0t)u(t); (e) sin ω0t; and (f) cos ω0t? P1.12 . For the systems describled by the equations below, with the input f(t) and output y(t), determine which of the system are linear and which are nonlinear. 2 dy(t) 2 dy(t) 2 dy(t)  (a) +2y(t)=f (t) (b) +3ty(t)=t f(t) (c)   +2y(t)=f(t) dt dt dt  dy(t) t (d) +y2 (t)=f(t) (e) 3y(t)+2=f(t) (f) y(t)=∫ f( τ)d τ dt −∞ dy(t) df(t) dy(t) df(t) (g) +() sint y(t)= +2f(t) (h) +2y(t)=f(t) dt dt dt dt Signal & Systems - FEEE, HCMUT – Semester: 02/10-11 Ch-1: Elementary of signal and system P1.13 . For the systems describled by the equations below, with the input f(t) and output y(t), determine which of the system are time- invariant parameter systems and which are time-varying parameter systems. (a) y(t)=f(t-2) (b) y(t)=f(-t) (c) y(t)=f(at) 5 2 (d) y(t)=tf(t-2) (e) y(t)= f( τ)d τ (f) y(t)= df(t)  ∫-5 dt  P1.14 . For the systems describled by the equations below, with the input f(t) and output y(t), determine which of the system are causal and which are noncausal. (a) y(t)=f(t-2) (b) y(t)=f(-t) (c) y(t)=f(at);a>1 (d) y(t)=f(at);a<1 Signal & Systems - FEEE, HCMUT – Semester: 02/10-11 5
4. Ch-1: Elementary of signal and system P1.18 . Suppose that a LTI system has the following output y(t) when the input is the unit step f(t)=u(t): y(t)=e -tu(t)+u(-1-t). Determine and sketch the response of the system to the input f(t) shown in Figure P1.18 P1.19 . A particular linear system has the property that the response to tk is cos(kt). What is the response of this system to the input: f(t) = π + 6t2− 47t 5 + et 6 Signal & Systems - FEEE, HCMUT – Semester: 02/10-11 Ch-1: Elementary of signal and system P1.20 . A continuous-time linear system with input f(t) and output y(t) yields the following input-output pairs: f(t) = ej2t→ y(t) = e j3t and f(t) = e−j2t→ y(t) = e − j3t a) If f 1(t)=cos(2t), determine the corresponding output y 1(t) for the system? b) If f 2(t)=cos(2(t-1/2)), determine the corresponding output y 2(t) for the system? Signal & Systems - FEEE, HCMUT – Semester: 02/10-11 7