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）︰ 97.11.20 考試時限（分鐘）： 120 是否需發放獎勵金： 是，謝謝^^ （如未明確表示，則不予發放） 試題 : 1.(25%) The power spectral density of a random process X(t) is shown as the figure, which consists of a delta function at f=0 and a triangular component (a) Please determine and sketch the autocorrelation function of X(t), R_X(τ) (b) What is the DC power in X(t)? (c) What is the AC power in X(t)? (d) What is the minimum sampling rate to result in uncorrelated samples of X(t)? Are these uncorrelated samples statistically independent? 圖: 橫軸是f，縱軸是S_X(f)，圖形是以(-f0,f0)為底，高為1，以原點為中心的三角形 　　　在f=0的地方有一個impulse，δ(f) 2.(25%) Consider a phase modulation (PM) system with modulated waveform defined as s(t) = AcCos[2πfc(t) + 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 canoncial form as n(t) = nI(t)cos[2πfc(t)] - nQ(t)sin[2πfc(t)]. Assuming ths CNR>>1, please determine (a) Output SNR (b) Figure of merit of the PM system (c) Compared with FM，what is kp in engineering meaning? Does PM have better performance than FM? 3.(25%+5%) In the figure of problem 1, if f0=4KHz，please answer the following questions. Please note the units. (a) What is minimum 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 adopt DPCM to save transmission bandwidth and rate by using 4 bits to represent the "difference" of samples, what is the resulting data rate? (d) DPCM is using similar principle like delta modulation. What are drawbacks for delta modulation? Are these drawbacks effect in DPAM? If yes, how to improve? If not, please explain the reason. (e) The voice signal has bandwidth similar to the case f0 = 4KHz. How can we develop stereo system using PCM and backwatd compatible to original PCM system? (5% bonus for this problem) 4.(25%+5%) The following questions are related to matched filter of baseband digital signaling. (a) For amplitude A and nit period T，please draw the waveforms for binary bi-phase level signaling (i.e. Manchester codes). (b) What is the impulse response of the matched filter of (a)? (c) Assuming bits 1110010 are transmitted using bi-phase level signaling and perfect timing alignment at the receiver (i.e. matched filter)，what is the block diagram of matched-filter receiver? Please draw the output waveform of this receiver. (d) Assuming AWGN with zero mean and 2-side power spectral density N0/2， and no signal strengeh loss in channel，please find the Eb/N0。 (e) From (c) with AWGN as (d)，please the receiver to properly decode the receivered wavegorm for "1" or "0"。 Please find the error probality with this receiver (using matched via Eb/N0。 ( 5%bonus ) --

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