Step 1.10 Now try plotting the following carrier waves with a(t) appearing on the left and b(t) appearing on the right. Place both plots onto a single graph as you did in steps 1.8 and 1.9. a(t) = 3sin(250t - ) b(t) = 8cos(500t + 0) Question 1.10 What are the differences between the two plots a(t) and b(t) from step 1.10? a. a(t) and b(t) have the same amplitudes b. a(t) has a higher frequency than b(t) c. a(t) and b(t) appear as identical plots d. For every single cycle for a(t), two cycles of b(t) are seen Plot 1.10 - Sine Cosine Wave Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 1.10 above into the IT300 Virtual Lab Plot Submission . Step 1.11 Set the phase angle of both sinusoidal equations to =0 radi 7 Part 2 Section 2.0: Amplitude Modulation message or modulating signal: m(t) = Amcos(2fmt) carrier: c(t) = Ac cos(2fct) modulation index: = Am/Ac, where 01 AM modulation formula: 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) Step 2.1 Open the MATLAB application Step 2.2 Click on the icon in the upper left on the "HOME" tab: "New Script"; the editor window should open. Step 2.3 In the editor window, type in the following and save: NOTE: when you save your MA 8 Ac: carrier amplitude Am: modulating signal's amplitude fc : carrier wave frequency in Hertz fm: modulating wave frequency in Hertz t: time range in seconds (start time 0 seconds, at 0.00001 second intervals, end time 0.003 seconds) m: formula for the modulating signal c: formula for the carrier wave mi: AM modulation index s: resulting modulated carrier wave or signal wave form Step 2.4 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. Fig 1. AM Modulation. The top left graph depicts the modulated signal wave 's'. Top right graph depicts the carrier wave. The lower right graph depicts the message or modulating wave form. Note1: If you do not see the figure above after you have executed the code, then recheck your code. Step 2.5 To better see how the modulated carrier is faithfully representing the message wave, lets combine the message and modulated carrier wave together on a single plot using the following code. 9 %AM Modulation; clear; Ac=5; Am=4; fc=10500; fm=1800; 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); yyaxis right; plot(t,s); title('combined message and signal'); 10 Figure 2. The lower right plot combines both message and modulated carrier signal onto the same plot for comparison. As can be seen, the signal wave changes coincide with the message wave changes. Therefore, by observation, we see that the signal faithfully represents the message wave. Step 2.5 Now change the message amplitude, Am, to 50 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), still behaves as an AM modulated signal, and therefore will faithfully represent the original message wave b. Very minimal changes in the signal, s(t), can be seen; however, it is difficult to clearly identify changes, which means that distortion is being experienced by our modulated carrier wave 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 Plot 2.5 AM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 2.5 above into the IT300 Virtual Lab Plot Submission . Step 2.6 Next, change the frequency of the message to fm=700 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. Plot 2.6 AM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 2.6 above