Frequency modulation, or FM, uses a wider bandwidth than amplitude modulation, or AM, but it is not affected as much by noise as AM is. The output of an FM transmitter is of the form

where m(t) is the message and νis a factor in Hz/volt if the units of the message are in volts.

(a) Create as message a signal

m(t) = cos(t)

Find the FM signal y(t) for ν = 10 and then for ν = 1. Use MATLAB to generate the different signals for times 0 ‰¤ t ‰¤ 10 at intervals of T_s = 0.01. Plot m(t) and the two FM signals (one for ν = 10 and the other for ν = 1) in the same plot. Is the FM transmitter a linear system? Explain.

(b) Create a message signal

Find the corresponding FM signal for ν = 1.

y(t) = cos(27t + 2n v | m(t)dt)| when m(t) > 0 when m(t) < 0 m1 (t) I|