[試題] 103-1 陳光禎 通信原理 期中考
課程名稱︰通信原理
課程性質︰選修
課程教師︰陳光禎
開課學院：電資學院
開課系所︰電機工程學系
考試日期（年月日）︰103.11.20
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
試題 :
1.[Gaussian Process,20%] Let X(t) be a zero-mean, stationary, Guassian process
with autocorrelation function R_x(τ).
(a)(5%)What is the power spectral density S_x(f)?
(b)(5%)By observing X(t) at some time t_k, what is the probabilty density
function in this observation? This process is applied to a square-law
device which is defined by the input-outout relation Y(t)=X^2(t), where
Y(t) is the output.
(c)(5%)Show that the mean of Y(t) is R_x(0).
(d)(5%)Show that the autocorrelation function of Y(t) is 2R_x(τ).
2.[PM,20%] Consider a phase modulation system, with the modulated waveform de-
fined by s(t)=A_c*cos[2πf_c*t+k_p*m(t)] where k_p is a constant and m(t) is
the message signal. The additive noise n(t) at the phase detector input can
be represented by the canonical form (i.e. I-channel and Q-channel).
Assuming the carrier-to-noise ratio at the detector input is high compared
with unity, please determine
(a)(8%)the ouput SNR
(b)(4%)the figure of merit of the system.
(c)(8%)Please derive the figure of merit for the FM system with sinusoidal
modulation, and compare the results.
3.[Waveform Coding,20%] A speech signal occupying bandwidth from 0-4kHz. We
wish to conduct digital communication for such signals. Please answer the
following series of questions.
(a)(5%)What is the Nyquist sampling rate in this case? What is the problem
if under-sampling?
(b)(5%)If we use 8 bits to represent a sample value, what is the data rate
for PCM?
(c)(5%)If we use delta modulation to encode such a signal, what is the mini-
mum rate if we use integer number of digits to represent a different sam-
ple?
(d)(5%)In case we are using DPCM and only need 4 bits to represent each of
the resulting sampling, what is the data rate for this DPCM?
4.[Rayleigh,20%] Consider a random process Z(t)=X(t)+jY(t)=R(t)exp(jΦ(t)),
where random process X(t) and Y(t) are statistically independent Gaussian
distributed with zero mean and variance σ^2 for any t. Please show that
R(t) is Rayleigh distributed and Φ(t) is uniformly distributed.
5.[Envelope Detection,20%] Consider the output of an envelope detector, which
is reproduced here for convenience
y(t)={[A_c+A_c*k_a*m(t)+n_I(t)]^2+[n_Q(t)]^2}^(1/2)
(a)(7%)Assume that the probability of the event |n_Q(t)|>ε*A_c*|1+k_a*m(t)|
is equal to or less than δ_1, where ε<<1. What is the probability that
the effect of the quadrature component n_Q(t) is negligible?
(b)(7%)Suppose that k_a is adjusted related to the message signal m(t) such
that the probability of the event A_c*[1+k_a*m(t)]+n_I(t)<0 is equal to
δ_2. What is the probability that the estimation y(t)≒A_c*[1+k_a*m(t)]
+n_I(t) is valid?
(c)(6%)Comment on the significance of the result in part (b) for the case
when δ_1 and δ_2 are both small compared with unity.
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※ 編輯: jerrysaikou (118.169.119.160), 11/21/2014 01:18:32
※ 編輯: jerrysaikou (118.168.115.50), 01/17/2015 16:45:07