所屬科目：中山◆電機◆通訊理論
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)?
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).
(a). (5%) Let.Prove that Φ1(t) andΦ2(t) are orthogonal for any fe
(b). (5%) Let p2 (t)=p1 (t-T). Show that Φ2(t)=Φ1(t-T) as fc is an integer multiple of 1/T.
(a). (5%) Combine all yk's with the coeficients ck, k = 1....M . We have Decide the maximum likelihood detector for u given the observation Y.
(b). (5%) What is the error probability Pe of the detector in (a)? Hiant: You can use Q-fumction, where
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. What is the sampling period
so that x(t) can be perfectly reconstructed by xp(t)?
with a fixed value of Φ. Show that W and Z have the same joint probability density
function (PDF).
.Prove that Φ1(t) andΦ2(t) are orthogonal for any fe
Decide the maximum likelihood detector for u given the observation Y.