107年 - 107 國立臺北大學_碩士班一般入學考試試題_通訊工程學系：通訊原理#147259

科目：【阿摩】未分類題庫 | 年份：107年 | 選擇題數：0 | 申論題數：19

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所屬科目：【阿摩】未分類題庫

選擇題 (0)

申論題 (19)

1. (10%) In wireless communication systems, Additive White Gaussian Noise (AWGN) channel is often assumed. What do "Additive", "White", and "Gaussian" mean?
2. (20%) Constellations with two kinds of labeling are show as below. Symbols from the left and right figure, respectively, are transmitted over the AWGN channel.

(a) \((3\%)\) How many information bits can be carried per symbol for the left figure?
(b) \((3\%)\) How many information bits can be carried per symbol for the right figure?
(c) \((7\%)\) Which labeling (left figure one or right figure one) will result in lower symbol error rate? Why?
(d) \((7\%)\) Which labeling will result in lower bit error rate? Why?
3. (10%) A matrix H for a linear block code is defined such that each vector v is a valid codeword if and only if Hv^T = 0.

Assume that $$H = \begin{bmatrix} 1 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 \end{bmatrix}$$.

(a) Is the vector \( v_{1} = [1\ 0\ 1\ 0\ 1\ 1] \) a valid codeword vector? Why or why not?
(b) How many valid codewords can be found?
4. (10%) Given φ₁(t) = 1, φ₂(t) = -t, φ₃(t) = 2t² - 1,

(a) Show that \(\varphi_1(t)\) and \(\varphi_2(t)\) are mutually orthogonal over the interval (-1, 1)
(b) Are \(\varphi_1(t)\) and \(\varphi_2(t)\) mutually orthogonal over the interval (-1, 1)? Why or why not?
5. (15%) Please answer the following questions with True(T) or False(F)

(a) \((3\%)\) The amplitude of Frequency Modulation (FM) is constant.
(b) \((3\%)\) The signal bandwidth of Amplitude Modulation (AM) is larger than FM.
(c) \((3\%)\) AM is an angle modulation scheme.
(d) \((3\%)\) For FM, the transmission power remains constant irrespective of modulation index.
(e) (3%) For Phase Modulation (PM), amplitude of carrier is varied according to the amplitude of modulation signals.
6. (10%) Prove the following Fourier transform operation.

$$v(t - \tau) \xrightarrow{F} e^{-j2\pi f\tau} \vec{V}(f)$$
7. (10%) A carrier is frequency modulated with a sinusoidal signal of 2 kHz resulting in a maximum frequency deviation of 5kHz. Find
(a) (5%) modulation index
(b) (5%) Bandwidth of the modulated signal
8. (15%) By giving the message m(t) and carrier A_c cos(2πf_c t)

(a) \((5\%)\) Find the amplitude-modulated signal
(b) \((10\%)\) Explain how to demodulate the signal of (a) by equations.