課程名稱︰信號與系統 課程性質︰大二必修 課程教師︰李琳山、李枝宏、陳宏銘、連豊力 開課學院：電資學院 開課系所︰電機系 考試日期（年月日）︰2015.04.20 考試時限（分鐘）：120分鐘 試題 : 2015 Signals & Systems Midterm 2015.04.20 09:10-11:10 two-sided A4 is allowed, calculators are not (the followings are retrieved from my memory, and therefore may be some minor mistakes.) 1.(15%) discrete-time, T=10 x(t) = 1 for |t|<=2 0 for 2<|t|<=5 x(t)=x(t+T) x(t) | x x x1 x x | | | | | ----------+----------t -2 -1 0 1 2 (a) find FT of x(t) (b) p(t) = 1 for -1<t<1 p(t) | +-+-+ | | | -------+-------t -1 0 1 find x(t)*p(t) 2.(12%) prove FT from FS 3.(5%*5) causal LTI y'' + 4y' + 3y = x' + 2x (a) draw block diagram with integrator, multiplier, adder (b) find H (c) find h (d) FIT? (e) causal? 4.(12%) (1) N=6 (2) x[0]+x[1]+...+x[5]=2 (3) (-1)^3x[0]+(-1)^4x[1]+...+(-1)^8x[5]=1 (4) x[n] has min energy in a period (still satisfies (1)-(3)) find x[n] 5.(4%*4) y[n]=(1/N)(x[n]+x[n-1]+...+x[n-(N-1)]) (a) linear? (b) memoryless? (c) time-invariant? (d) stable? 6.(10%) {a_k} = coefficients of x[n] define x_(m)[n]=x[n/m] for n=integral*m 0 otherwise find coefficients for this new function 7.(10%) y(t) = integral(-infinity,t) (t-tau+2)x(tau) d(tau) (a) impulse response? (b) for 1<=t<=2, find y(t) for x(t) = u(t)-u(t-1) --

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