(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?

(a)(6%) (* 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)

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

(b) (3 %) How do we sample y(t) properly to avoid the aliasing effiect?

(a) (6%)

(b)(6%)

(a) (5%) What does the unique decodability mean? Assume that a code has the property thatfor each . 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 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 length? Clearly state your coding strategy.

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