Lab 3
##Exercise 1 - FM Modulator
In this exercise we were implementing frequency modulation (FM), which is given by the general equation:
In this lab we were using the equivalent form:
The modulation index of an FM signal is given by:
The finished diagram is below:
In this VI we converted the message waveform to an array so we could integrate it and add in the delta f part to create theta(t). We also used a sine/cosine function to get cos(theta(t)) and sin(theta(t)), which could then be multiplied by the carrier signal. We used a message signal of 1kHz and carrier of 10kHz, with delta f set to 500 initially. The results are shown below:
###Screenshot 1 - Panel view with delta f = 500.
Here because delta f is very small, it is difficult to see the frequency variation in the time domain plots. However, we can clearly see in the PSD that there is a major peak at 10kHz with sidebands at 9kHz and 11kHz. This looks similar to AM, but with the lower sideband out of phase by 180 degrees. The modulation index in this case is 0.5. Next we tried a value for delta f of 2000:
###Screenshot 2 - Panel view with delta f = 2000.
Here it is slightly easier to see the frequency variation in the time domain signal. Now we have a modulation index of 2, and as this increases we see more sidebands at 8kHz, 9kHz, 11kHz and 12kHz, each spaced 1kHz apart. The magnitude of the peak at 10kHz has also dramatically been reduced. Next we changed delta f to 5000:
###Screenshot 3 - Panel view with delta f = 5000.
Now the frequency variation is really clear in the time domain. The PSD of the signal is also interesting, with even more sidebands at frequencies spaced 1kHz apart from ~3kHz - 18kHz. We can see that as we increase delta f, the bandwidth of the signal increases (Carson's Rule).
##Exercise 2 - FM Demodulator