essentials of communication systems engineering (page 167쪽 문제 3.4 풀이와 매틀랩)

소개

essentials of communication systems engineering (john G. Proakis masoud salehi)
page 167쪽 문제 3.4 풀이와 이에대한 매틀랩 구현. 그리고 자세한 분석.

목차

problem 3.4 Demodulation of the DSB-AM Signal

The message signal m(t), which is given in Problem CP-3.1 ( m(t) = sinc(100t), 0≤t≤to ), modulates the carrier c(t) = cos2πfct and results in the DSB-AM signal u(t) = m(t)c(t).
The carrier frequency fc = 250Hz and to = 0.1.
1. By selecting the sampling interval ts = 0.0001, generate 1000 samples of the message signal m(t), the modulated signal u(t), and plot both signals.
2. Demodulate the sampled DSB-AM signal u(t) generated in Part 1 by using the demodulator shown in Figure CP-3.4. Perform the demodulation for Φ = 0, π/8, π/4, π/2, and plot the received message signal mr(t). The lowpass filter is a linear-phase-FIR filter having 31 taps, a cutoff frequency (-3dB) of 100Hz, and a stopband attenuation of at least 30dB.
3. Comment on the results obtained in Part 2.
4. Instead of using a time-domain-lowpass filter to reject the frequency components centered at 2fc, compute the discrete-Fourier transform(DFT) of 1000 samples of the mixer output, set to zero those frequency components centered at 2fc and compute the inverse DFT to obtain the time-domain signal. Compare the results of this frequency-domain filtering with the time-domain filtering in Part 2.

- page 167쪽 문제 3.4 풀이

- 매틀랩 소스와 구현 그래프. 그리고 분석

본문내용

t=0:0.0001:0.1; % t sampled with sampling interval 0.0001
fc=250; % carrier frequnecy
mt=sinc(100*t); % sampled message signal
ct=cos(2*pi*fc*t); % sampled carrier signal
ut=mt.*ct; % sampled DSB-AM signal
stem(t,mt,`b`); % ploting the sampled message signal using stem version
hold on
stem(t,ut,`r`); % ploting the sampled DSB-AM signal using stem version
▶ 어느 임의의 부분을 확대 하여서 보았다. stem 함수를 이용하였기 때문에 확대하여서 보면 확실하게 m(t)하고 u(t)가sampling 되었다는 것을 알 수가 있다.

2.
① ø=0
t=0:0.0001:0.1; % t sampled with sampling interval 0.0001
fc=250; % carrier frequnecy
mt=sinc(100*t); % sampled message signal
ct=cos(2*pi*fc*t); % sampled carrier signal
ut=mt.*ct;
phi=0; % sampled DSB-AM signal

mt1=ut.*cos(2*pi*fc*t+phi); % mixed signal when the phase is 0

h=fir1(30,0.2); % impulse response of LPF with 31 taps and 100Hz frequency response

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