Issue with demonstrating amplitude modulation of sinusoid using MatLab I am trying to demonstrate Conventional and DSB-SC modulation of a signal $ \sin(2\pi1000t) $ using MatLab. My carrier signal is $ \sin(2\pi f_ct)$ where $f_c = 100\text{ MHz}$. Now according to theory, after modulation, the modulated signal should have a spectrum same as that of message signal shifted to the frequency of carrier on both sides. But I am getting the plot as that of the carrier signal in the frequency domain.
This is the code that I am using for DSB-SC modulation
% CODE FOR PLOTTING MESSAGE SIGNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%

Fs = 20*100*10^6/3;
Fm = 1000; %Hz
t = 0:1/Fs:0.005-1/Fs;

Am = 1;

m = Am*sin(2*pi*Fm*t);

temp = size(m);
N = temp(2);

f = -Fs/2:Fs/(N-1):Fs/2;

M = fftshift(fft(m));
figure(1)
plot(f,abs(M))
grid('on')
title('Message signal')
xlabel('Frequency in Hertz') 
ylabel('|M(F)|') 

% CODE FOR PLOTTING CARRIER SIGNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Fc=100*10^6;%100 MHz

Fs = 20*Fc/3;
Ac = 1;%amplitude
c = Ac*sin(2*pi*Fc*t);

temp = size(c);
N = temp(2);

f = -Fs/2:Fs/(N-1):Fs/2;

C = fftshift(fft(c));
figure(2)
plot(f,abs(C))
grid('on')
title('Carrier signal')
xlabel('Frequency in Hertz') 
ylabel('|C(F)|')

% CODE FOR PLOTTING DSB-SC MODUALTED SIGNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

s = Ac*m.*sin(2*pi*Fc*t);

temp = size(s);
N = temp(2);

f = -Fs/2:Fs/(N-1):Fs/2;

S = fftshift(fft(s));
figure(3)
plot(f,abs(S))
grid('on')
title('DSB-SB Modulated signal')
xlabel('Frequency in Hertz') 
ylabel('|S(F)|')


And this is the spectrum of $S(f)$ in code. As you can see. there are only two peaks, one at $+f_c$ and one at $-f_c$(not shown in figure). But in reality, it should have been 2 peaks at $f_c+f_m , f_c-f_m$ and two peaks at $-f_c-f_m,-f_c+f_m$. So what is going wrong here? How can I fix this?
The problem is lack of frequency resolution in your plot. What you are seeing is in fact the two sidebands. Just zoom in to see them:

My advice is to use a much lower carrier frequency, such as 10 kHz. Doing so will make it much easier to study this modulation in Matlab, without sacrificing anything essential.