私立中原大學八十八學年度博士班招生考試命題紙

所組別：

電子工程學系博士班甲組

科目：

通訊系統

考試時間：

06月09日第 1節

1. Consider a (7,4) Hamming code with the generator matrix G is gven by

   (a)	Construct the eight code words in the dual code. (10%)
   (b)	Find the minimum distance of the dual code detemined in part(a). (10%)

   
   
   
2. The signal vectors S₁ and S₂ are used to represent binary symbols 1 and 0, respectively, in a coherent binary FSK system. The receiver decides in factor of symbol 1 when X^TS₁ < X^TS₂. Where X^TS_i is the inner product of the observation vector X and the signal vector S_i where i=1,2 . Show that this decision rule is equivalent to the condition X₁> X₂, where X₁ and X₂ are the elements of the observation vector X. Assume that the signal vectors S₁ and S₂ have equal energy. (20%)
   
   
3. Given the definition of (a) MPSK.(b) MFSK. (c) MASK. (20%)
   
   
4. If the Fourier transform of the message signal m(t) is

   (a)	Draw the signal spectrum S(f) of (1) AM. (2) DSB-SC. (3) VSB. (15%)
   (b)	Can m(t) be modulated as a SSB? Why? (5%)

   
   
   
5. Prove the autocorrelation function has its maximum magnitude at . (20%)

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