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

1. (10%) In wireless communication systems, Additive White Gaussian Noise (AWGN) channel is often assumed. What do "Additive", "White", and "Gaussian" mean?

(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?

(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?

(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?

(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. $$v(t - \tau) \xrightarrow{F} e^{-j2\pi f\tau} \vec{V}(f)$$

(a) (5%) modulation index

(b) (5%) Bandwidth of the modulated signal

(a) \( (5\%) \) Find the amplitude-modulated signal

(b) \( (10\%) \) Explain how to demodulate the signal of (a) by equations.