1. GoldExperience 통신공학설계실험 2003440033 Kim Hyun Tai
Kim Jung Woo
Kim Dae Hyun

2. triangle함수(1) function x=triangle(tau, T1, T2, fs, df) %
%*************************************************
% Generation of triangular pulse
% tau : pulse width [sec]
% fs : sampling frequency
% fs must be greater than or equal to 2/T
% [T1, T2] : observation time interval [sec]
% df : frequency resolution [Hz]
% example
% x=rect(2, -5, 5, 10, 0.01)
%************************************************** 2

3. triangle함수(2) %clear %tau=2; %T1=-5; T2=5;
%df=0.01; %frequency resolution
%fs=10; %sampling frequency
ts=1/fs; %sampling period
t=[T1:ts:T2]; %observation time interval 3

4. triangle함수(3) % Signal genaration of triangular pulse
x=zeros(size(t));
midpoint=floor((T2-T1)/2/ts)+1;
L1=midpoint-fix(tau/2/ts);
L2=midpoint+fix(tau/2/ts)-1;
x(L1:midpoint)=(2/tau)*t(L1:midpoint)+1; %2/tau is the slope
x(midpoint+1:L2)=-(2/tau)*t(midpoint+1:L2)+1;
%[X,x1,df1]=fftseq(x,ts,df);
%X1=X/fs; %scaling
%f=[0:df1:df1*(length(x1)-1)]-fs/2; %frequency vector (range to plot)
%plot(t,x); axis([T1, T2 -2 4]) 4

5. DSB_SC (1) % DSB_SC.m % Matlab program example for DSBSC-AM modulation
% The message signal is triangular pulse with pulse width tau=0.1 %
clear
echo on
df=0.3; % desired frequency resolution [Hz]
ts=1/1000; % sampling interval [sec]
fs=1/ts; % sampling frequency
fc=250; % carrier frequency
T1=-0.1; T2=0.1; % observation time interval (from T1 to T2 sec)
t=[T1:ts:T2]; % observation time vector
N = length(t);
snr=20; % SNR in dB (logarithmic)
snr_lin=10^(snr/10); % linear SNR 5

6. DSB_SC (2) % message signal tau=0.1; % Pulse width [sec]
x=triangle(tau, T1, T2, fs, df);
xc=cos(2*pi*fc.*t); % carrier signal
xm=x.*xc; % mixing (xm is modulated signal)
[X,x,df1]=fft_mod(x,ts,df); % Fourier transform of message signal
X=X/fs; % scaling
f=[0:df1:df1*(length(x)-1)]-fs/2; %frequency vector (range to plot)
[Xm,xm,df1]=fft_mod(xm,ts,df); % Fourier transform of modulated signal
Xm=Xm/fs; % scaling
[XC,xc,df1]=fft_mod(xc,ts,df); % Fourier transform of carrier
signal_power=norm(xm(1:N))^2/N; % power in modulated signal
noise_power=signal_power/snr_lin; % compute noise power
noise_std=sqrt(noise_power); % compute noise standard deviation
noise=noise_std*randn(1,length(xm)); % generate noise 6

7. DSB_SC (3) r=xm+noise; % add noise to the modulated signal
[R,r,df1]=fft_mod(r,ts,df); % spectrum of the signal+noise
R=R/fs; % scaling
%pause % Press a key to show the modulated signal power
signal_power
pause % Press any key to see the message signal waveform
clf %
% Time domain waveforms of message signal and modulated signal
subplot(2,1,1)
plot(t,xc(1:length(t)))
xlabel('Time')
title('Carrier waveform') 7

8. DSB_SC (4) subplot(2,1,1) plot(t,x(1:length(t))) xlabel('Time')
title('Message signal')
pause % Press any key to see the modulated signal waveform
subplot(2,1,2)
plot(t,xm(1:length(t)))
title('Modulated signal')
pause % Press any key to see the spectra %
% Frequency domain plots of signal spectral
plot(f,abs(fftshift(X)))
xlabel('Frequency‘) 8

9. DSB_SC (5) title('Spectrum of the message signal') subplot(2,1,2)
plot(f,abs(fftshift(Xm)))
title('Spectrum of the modulated signal')
xlabel('Frequency')
pause % Press a key to see a noise sample %
% Waveform and spectrum of signal plus noise
clf
subplot(2,1,1)
plot(t,noise(1:length(t)))
title('noise sample')
xlabel('Time')
pause % Press a key to see the modulated signal and noise 9

10. DSB_SC (6) plot(t,r(1:length(t))) title('Signal and noise')
xlabel('Time')
pause % Press a key to see spectra of modulated signal and noise
subplot(2,1,1)
plot(f,abs(fftshift(Xm)))
title('Signal spectrum')
xlabel('Frequency')
subplot(2,1,2)
plot(f,abs(fftshift(R)))
title('Signal and noise spectrum') 10

11. PLOT 결과(1)
그림1
그림2 11

12. PLOT 결과(2)
그림1
그림2 12

13. PLOT 결과(3)
그림1
그림2 13

14. PLOT 결과(4)
그림1
그림2 14

15. PLOT 결과(5) 15

16. DSBSC_DEM (1) % DSBSC_DEM.m
% Matlab program example for DSBSC-AM demodulation
% The message signal is triangular pulse with pulse width tau=0.1
clear
echo on
df=0.3; % desired frequency resolution [Hz]
ts=1/1500; % sampling interval [sec]
fs=1/ts; % sampling frequency
fc=250; % carrier frequency
T1=-0.1; T2=0.1; % observation time interval (from T1 to T2 sec)
t=[T1:ts:T2]; % observation time vector %
% modulation : DSB-SC
tau=0.1; % Pulse width [sec]
x=triangle(tau, T1, T2, fs, df); % message signal 16

17. DSBSC_DEM (2) %x=rect(tau, T1, T2, fs, df); % message signal
xc=cos(2*pi*fc.*t); % carrier signal
xm=x.*xc; % mixing (xm is modulated signal)
[X,x,df1]=fft_mod(x,ts,df); % Fourier transform of message signal
X=X/fs; % scaling
[Xm,xm,df1]=fft_mod(xm,ts,df); % Fourier transform of modulated signal
Xm=Xm/fs; % scaling
[XC,xc,df1]=fft_mod(xc,ts,df); % Fourier transform of carrier
clf
f=[0:df1:df1*(length(xm)-1)]-fs/2; %frequency vector (range to plot)
subplot(2,1,1)
plot(t,x(1:length(t)))
%xlabel('Time')
title('Message signal')
subplot(2,1,2) 17

18. DSBSC_DEM (3) plot(t,xm(1:length(t))) xlabel('Time')
title('Modulated signal')
pause % Press any key to see the spectra
subplot(2,1,1)
plot(f,abs(fftshift(X)))
%xlabel('Frequency')
title('Spectrum of the message signal')
subplot(2,1,2)
plot(f,abs(fftshift(Xm)))
title('Spectrum of the modulated signal')
xlabel('Frequency') %
% AWGN noise channel
%signal_power=norm(xm(1:N))^2/N; % power in modulated signal
%noise_power=signal_power/snr_lin; % compute noise power 18

19. DSBSC_DEM (4)
%noise_std=sqrt(noise_power); % compute noise standard deviation
%noise=noise_std*randn(1,length(xm)); % generate noise
%r=xm+noise; % add noise to the modulated signal
r=xm; % received signal (r=rx for distortionless channel)
[R,r,df1]=fft_mod(r,ts,df); % spectrum of the received signal
R=R/fs; % scaling %
% demodulation : coherent detection
% We use ideal lowpass filter in this example.
y=r.*xc; % mixing
[Y,y,df1]=fft_mod(y,ts,df); % Fourier transform of mixer output
Y=Y/fs; % scaling
f_cutoff=150; % cutoff frequency of the filter
n_cutoff=floor(f_cutoff/df1); % design the filter 19

20. DSBSC_DEM (5) H=zeros(size(f));
H(1:n_cutoff)=2*ones(1,n_cutoff); % freq. response of the lowpass filter
H(length(f)-n_cutoff+1:length(f))=2*ones(1,n_cutoff); % note that the filter is periodic
Z=H.*Y; % spectrum of the filter output
z=real(ifft(Z))*fs; % filter output waveform
pause % Press a key to see the effect of mixing
clf
subplot(3,1,1)
plot(f,fftshift(abs(X)))
title('Spectrum of the the Message Signal')
%xlabel('Frequency')
subplot(3,1,2)
plot(f,fftshift(abs(R)))
title('Spectrum of the Received Signal') 20

21. DSBSC_DEM (6) %xlabel('Frequency') subplot(3,1,3)
plot(f,fftshift(abs(Y)))
title('Spectrum of the Mixer Output')
xlabel('Frequency')
pause % Press a key to see the effect of filtering on the mixer output
clf
subplot(3,1,1)
subplot(3,1,2)
plot(f,fftshift(abs(H)))
title('Lowpass Filter Characteristics') 21

22. DSBSC_DEM (7) plot(f,fftshift(abs(Z)))
title('Spectrum of the Demodulator output')
xlabel('Frequency')
pause % Press a key to compare the spectra of the message an the received signal
clf
subplot(2,1,1)
plot(f,fftshift(abs(X)))
title('Spectrum of the Message Signal')
%xlabel('Frequency')
subplot(2,1,2)
title('Spectrum of the Demodulator Output')
pause % Press a key to see the message and the demodulator output signals 22

23. DSBSC_DEM (8) plot(t,x(1:length(t))) title('The Message Signal')
%xlabel('Time')
subplot(2,1,2)
plot(t,z(1:length(t)))
title('The Demodulator Output')
xlabel('Time') 23

24. PLOT 결과(1)
그림1
그림2 24

25. PLOT 결과(2)
그림1
그림2 25

26. PLOT 결과(3) 26

27. PLOT 결과(4) 27

28. PLOT 결과(5) 28

29. PLOT 결과(6) 29

30. COMPUTER EXERCISES(2.1)
% ce2_1: Computes generalized Fourier series coefficients for exponentially
% decaying signal, exp(-t)u(t), or sinewave, sin(2*pi*t) %
tau = input(¡¯Enter approximating pulse width: ¡¯);
type_wave = input(¡¯Enter waveform type: 1 = decaying exponential; 2 = sinewave ¡¯);
if type_wave == 1
t_max = input(¡¯Enter duration of exponential: ¡¯);
elseif type_wave == 2
t_max = 1;
end
clf
a = [];
t = 0:.01:t_max;
cn = tau;
n_max = floor(t_max/tau)
for n = 1:n_max 30

31. COMPUTER EXERCISES(2.1) LL = (n-1)*tau; UL = n*tau; if type_wave == 1
a(n) = LL, UL);
elseif type_wave == 2
a(n) = LL, UL);
end
disp(¡¯ ¡¯)
disp(¡¯c_n¡¯)
disp(cn)
disp(¡¯Expansion coefficients (approximating pulses not normalized):¡¯)
disp(a)
x_approx = zeros(size(t));
for n = 1:n_max 31

32. COMPUTER EXERCISES(2.1) x_approx = x_approx + a(n)*phi(t/tau,n-1); end
if type_wave == 1
MSE = 0, t_max) - cn*a*a¡¯;
elseif type_wave == 2
MSE = 0, t_max) - cn*a*a¡¯;
disp(¡¯Mean-squared error:¡¯)
disp(MSE)
disp(¡¯ ¡¯)
plot(t, x_approx), axis([0 t_max -inf inf]), xlabel(¡¯t¡¯),
ylabel(¡¯x(t); x_a_p_p_r_o_x(t)¡¯)
hold
plot(t, exp(-t))
title([¡¯Approximation of exp(-t) over [0, ¡¯,num2str(t_max),¡¯] with
contiguous rectangular pulses of width ¡¯,num2str(tau)]) 32

33. COMPUTER EXERCISES(2.1) elseif type_wave == 2
plot(t, x_approx), axis([0 t_max -inf inf]), xlabel(¡¯t¡¯),
ylabel(¡¯x(t); x_a_p_p_r_o_x(t)¡¯)
hold
plot(t, sin(2*pi*t))
title([¡¯Approximation of sin(2*pi*t) over [0, ¡¯,num2str(t_max),¡¯] with
contiguous rectangular pulses of width ¡¯,num2str(tau)])
end
% Decaying exponential function for ce_1 %
function z = integrand_exp(t)
z = exp(-t);
% Sine function for ce_1
function z = integrand_sine(t)
z = sin(2*pi*t);
% Decaying exponential squared function for ce_1 33

34. COMPUTER EXERCISES(2.1) % function z = integrand_exp2(t)
z = exp(-2*t);
% Sin^2 function for ce_1
function z = integrand_sine2(t)
z = (sin(2*pi*t)).^2;
A typical run follows:
>> ce2_1
Enter approximating pulse width: 0.125
Enter waveform type: 1 = decaying exponential; 2 = sinewave: 2
n_max = 8
c_n
0.1250
Expansion coefficients (approximating pulses not normalized): 34

35. PLOT 결과 35

36. Goldexperience
감 사 합 니 다 36