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110年 - 110 國立中山大學_碩士班招生考試_電機系(戊組)、通訊所(甲、乙組)、電波聯合：通訊理論#104364
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1.(30%) Short answer questions.
(a). (10%) Explain the sampling theory.
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(b). (10%) What is the Nyquist criterion?
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(c). (5%) What is color noise?
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(d). (5%) Explain why the matched filter is optimum in the additive white Gaussian noise (AWGN) channel.
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(a). (10%) Is x(t) a periodic signal? Justify your answer.
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(b). (5%) Compute the Fourier transform of h(t).
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(c). (10%) Is x(t)*h(t) a periodic signal? Provide your reason. and assume
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3.(5%) Consider a signal x(t)=u(t+To)-u(t-T0), where u(t) is the unit step function. Performing the impulse-train sampling on x(t), we can have. What is the sampling period so that x(t) can be perfectly reconstructed by xp(t)?
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4. (10%) Assume that we have a complex-value Gaussian random variable Z = X+ jY, where Xand Y are independent identically distributed random variables with zero mean and variance σ2. Suppose with a fixed value of Φ. Show that W and Z have the same joint probability density function (PDF).
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(a). (5%) Let.Prove that Φ1(t) andΦ2(t) are orthogonal for any fe
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(b). (5%) Let p2 (t)=p1 (t-T). Show that Φ2(t)=Φ1(t-T) as fc is an integer multiple of 1/T.
#441817
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110年 - 110 國立中山大學_碩士班招生考試_電機系(戊組)、通訊所(甲、乙組)、電波聯合：通訊理論#104364
110年 · #104364
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