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110 年 - 110 國立臺灣大學_碩士班招生考試_電信工程研究所乙組:通信原理(含信號與系統)#101261 

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1.(1) (12 %) Illustrate the following four terms: (a) aliasing efiect; (b) LTI; (c) wide-sense stationary random process; (d) additive white Gaussian noise


(2) (6 %) Suppose that the continuous-time Fourier transform of x(t) is X(jω). What is the Fourier transform of Re(x(-2t+3) I where Tef ; means taking the real part?


(3) Determine the following convolutions

【題組】(a)(6%) 614157c7064a5.jpg (* means the discrete convolution and 4[n] is the unit step function)


(b) (6%) [cos(πt) +sin(4πt)+ cos(10πt)]* sinc(21) (* means the continuous convolution)


(4) Suppose that x(t) is real and has the bandwidth of W and
6141584117dd5.jpgwhere *means convolution.

【題組】(a) (5%) What is the bandwidth of y(t)?

6.【題組】(b) (3 %) How do we sample y(t) properly to avoid the aliasing effiect?


(5) Find the inverse Z transform of the following functions (suppose that x[r] is causal).

【題組】 (a) (6%) 6141587536837.jpg


(b)(6%) 614158f3188d1.jpg


(6) (25%) Consider a discrete memoryless source (DMS) with the associated source alphabet X := {a, b, c, d, e,f, g}. Each source output is independenty selocted from C with the probability distribution Px given in Table 1. The goal of source coding for the DMS is to construct a code C that assigns cach symbol 6141596034d42.jpgbit string6141599e59adb.jpgN. Its average length is defined as614159cd63d70.jpgMoreover, the code is usually required to be uniquely decodable. 614159fb65435.jpg  Please answer the following questions.


(a) (5%) What does the unique decodability mean? Assume that a code has the property that61415a35c3412.jpgfor each 61415a589baf8.jpg. Is the code uniquely decodable?


(b) (5%) A class of codes called the prefix-free codes can be decoded with no delay (hence sometimes also called instantareous codes). What is the definition for the prefix-free codes?
 Every prefix-free code for the alphabet 9X with its codeword lengths 61415aa40100f.jpg must satisfy the Kraftinequality. What is the Kraft inequality?
Assume that a code with its codeword lengths satisfies the Kraft inequality. Is it uniquely decodable? Does a uniquely decodable code have to satisfy the Kraft inequality?


(c) (10%) Use the Hufiman algorithm to construct a prefix-free code for the above mentioned DMS. What is the associated average length61415ad6addcd.jpg? Clearly state your coding strategy.

12.【題組】(d) (5%) Explain why the Huffman algorithm gives an optimal source code, i.e. no other source coding strategy has smaller61415ad6addcd.jpg.


(7) (25%) Consider a standard M-ary digital modulation scheme where the signal space diagram is spanned by two orthonormal waveforms, i.e. each symbol on the constellation has the in-phase and quadrature-phase components. Assume that the underlying channel model is additive white Gaussian noise (AWGN) with the power spectral density N0 / 2 , and that no inter-symbol interference is happening. Further, assume that all symbols on the constellation are equally probable. Please answer the following questions.

【題組】 (a) (5%) Using the signal space diagrams given in Figures la and 1b, respectively. Which one has the better performance (i.e. the smallest symbol error probability)? Explain your reason.


(b) (10%) Derive the optimal symbol error probability when using the signal space diagram given in Figure I b in terms of the average symbol energy, No, and the Q-function,


(c) (5%) Given an arbitrary M-ary modulation scheme with the minimum distance61415b98747ed.jpg, derive a union upper bound for the symbol error probability in terms of 61415b98747ed.jpg and the Q-function.


(d) (5%) Since the minimun distance of a constellation dominates the performance of a modulation scheme, one would desire a signal diagram with the same minimum distance61415bd61d4cd.jpg constraint that has smaller average symbol energy. Please design a 7-ary signal diagram on the I/Q-constellation with 61415bd61d4cd.jpg = 2 and its average symbol energy no larger than 3.43. red



15. 設 a 為正數,若 x2 - 2x - a 可分解為兩個 x 的一次式,則 a 不可能為下列哪一個數? (A)2 × 3 × 5 × 6 (B)2 × 3 × 4 × 5 (C)3 × 4 × 5 × 6 (D)4 × 5 × 6 × 7 ...

50 x


110 年 - 110 國立臺灣大學_碩士班招生考試_電信工程研究所乙組:通信原理(含信號與系統)#101261-阿摩線上測驗

110 年 - 110 國立臺灣大學_碩士班招生考試_電信工程研究所乙組:通信原理(含信號與系統)#101261