課程名稱︰通信原理
課程性質︰電機系複選必修
課程教師︰陳光禎
開課學院：電資學院
開課系所︰電機系
考試日期（年月日）︰2009/11/12
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(25%) Let X(t) be a random noise process with autocorrelation function
Rx(τ)=(No/2)δ(τ).
(a) Is X(t) a white noise ? Is X(t) zero-mean? Please state the reason.
(b) If X(t) is applied to an ideal band-pass filter with center frequency
fc and two-side bandwidth B,what is the total noise power at the output of
the filter?
(c) What is the autocorrelation function of output process from this ideal
band-pass filter in (c)?
(d) Suppose Y(t)=X^2(t) is AWGN with zero mean and 2-side p.s.d No/2 .
Then,what is the autocorrelation of Y(t),RY(τ)?
2.(20%) The signal sideband version of angle modulation is defined by
^
s(t)=exp[-ψ(t)]cos[2πfct+ψ(t)]
^
where ψ(t) is the Hilbert transform of the phase function ψ(t),and fc is
the carrier frequency.
(a) Show that the spectrum of the modulated signal s(t) contains no frequency
components in the interval -fc<f<fc , and is of infinite extent .
(b) Give that the phase function
ψ(t)=βsin(2πfmt)
where β is the modulation index and fm is the modulation frequency,derive
the corresponding expression for the modulated wave s(t) .
3. (15%) Consider a phase modulation (PM) system with modulation waveform
defined as s(t)=Ac{cos[2πfct+kpm(t)]},where kp is a constant and m(t) is
the message signal . The additive noise n(t) at the phase detector input has
the cononcial form as n(t)=ni(t)cos(2πfct)-nqsin(2πfct) . Assuming the
CNR>>1 , please determine
(a) Output SNR
(b) Figure of merit of the PM system
4. (20%) In the figure of problem 1, if fo=4KHz,pleasw answer the following
questions.Please note the units.
(a) What is the minimun sampling rate?
(b) If we want to use PCM to represent in digital signaling format and 8 bits
to represent a sample , what is the data rate?
(c) If we want to minimize data rate and decide to employ delta modulation,
please explain how delta modulation works.
(d) What are the challenges for delta modulation , and how to improve ?
(圖為底長度為fo之等腰三角形,高度為No/2)
5. (20%) The following questions are related to matched filter of baseband
digital signaling.
(a) For signaling as the following figure of symbol period T , please design
the matched filter receiver, and explain how it works by drawing waveform of
input/output of matched filter.
(b) If the signal transmission in channel is embedded in AWGN with AWGN with
zero mean and 2-side p.s.d No/2 without other noise nor distortion,please
derive the BER in (a).
(圖: Signal"1" 為在時間軸上從0開始到T , 底的長度為T高度為A之等腰三角形
Signal"0" 為在時間軸上從0開始到T , 底的長度為T高度為-A之等腰三角形)
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※ 編輯: lk806 來自: 140.112.243.69 (11/12 20:38)