message or modulating signal:

carrier: modulation index: AM modulation formula:

m(t) = Amcos(2fmt) c(t) = Ac cos(2fct) = Am/Ac, where 01 s(t) = Ac[1 + cos(2fmt)] cos(2fct)

Plot the following equations: m(t) = 4cos(2*1800Hz*t) c(t) = 5cos(2*10.5kHz*t)

= 4/5 = 0.8 s(t) = 5[1 + 0.8cos(2*1800Hz*t)]cos(2*10.5kHz*t)

%AM Modulation; 

clear; Ac=5; Am=4; fc=10500; fm=600; t=0:0.00001:0.003; m=Am*cos(2*pi*fm*t); c=Ac*cos(2*pi*fc*t); mi = Am/Ac;

s=Ac*(1+mi*cos(2*pi*fm*t)).*cos(2*pi*fc*t);

subplot(2,2,1);

 plot(t,s); xlabel('time'); ylabel('amplitude'); title('AM modulation'); subplot(2,2,4); plot(t,m); xlabel('time'); ylabel('amplitude'); title('Message'); subplot(2,2,2); 

 plot (t,c); xlabel('time'); ylabel('amplitude'); title('Carrier'); 

Select the "Run" icon. Another window should open (fig.1) showing graphical plots for the modulated carrier wave or signal, and the message or modulating wave.

Step 2.5 To better see how the modulated carrier is faithfully representing the message wave, letscombine the message and modulated carrier wave together on a single plot using the following code.

%AM Modulation; 

clear; Ac=5; Am=4; fc=10500; fm=600; t=0:0.00001:0.003; m=Am*cos(2*pi*fm*t); c=Ac*cos(2*pi*fc*t); mi = Am/Ac; s=Ac*(1+mi*cos(2*pi*fm*t)).*cos(2*pi*fc*t); subplot(2,2,1);

plot(t,s); xlabel('time'); ylabel('amplitude'); title('AM modulation'); subplot(2,2,4); plot(t,m); xlabel('time'); ylabel('amplitude'); title('Message'); subplot(2,2,2); 

plot (t,c); xlabel('time'); ylabel('amplitude'); title('Carrier'); subplot(2,2,3); yyaxis left; plot(t,m); 

ylim([-40 40]) yyaxis right; plot(t,s); ylim([-40 40]) title('combined message and signal'); 

Now change the message amplitude, Am, to 30 and plot signal. Answer the following question.

Question 2.5 Having changed the message amplitude to Am=50, select the correct statement

a. The signal, s(t), faithfully represents the original message wave m(t) b. It is more difficult to clearly see a correlation between changes in m(t) and s(t); as such

distortion is being experienced by the modulated carrier wave s(t) c. Since only the amplitude of the message wave has increased, there is no negative impact to

the modulated carrier signal d. None of the above are correct

Step 2.6 Next, change the frequency of the message to fm=1700 and the message amplitude to Am=5. Make sure to plot the combined message and modulated carrier signal onto a single plot using the MatLab code above.

Question 2.6 Select the correct statement that describes what you see in the plots:

a. The signal, s(t), is distorted by the dramatic change in message frequency. b. The message amplitude change can be seen in the signal plot of s(t). When comparing plots

for s(t) and m(t), it is obvious that the signal accurately represents the message. c. Both the message and carrier frequencies increase, therefore distortion will be experienced. d. The phase of the signal has shifted to the right, because AM techniques impact phase and

amplitude.