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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※ 編輯: srchen95 (60.245.65.133), 04/20/2015 13:57:30