Execute the provided MATLAB program fm_example. Note that this program also calls MATLAB functions that were provided in Modules 2 and 3, so you need to have these available as well. This program loads a built-in sound file of a train whistle which lasts approximately 1.6 seconds. The program plays the train whistle through the speakers. You should hear two bursts, each of which sounds like a musical chord (this is actually a slightly out-of-tune D minor chord for you musicians). The program then displays the time function and the frequency domain approximation of the signal in figure 1. The train whistle is then upsampled to a higher sampling rate and replayed. The result is shown in figure 2. The signal is then modulated to a carrier using DSB-SC (figure 3), demodulated using the same carrier (figure 4), and filtered (figure 5). The demodulated and filtered signal is played through the speakers again. Do you hear a difference?
Use the zoom, pan, and cursor controls on the graphics windows to answer the following questions:
What are the frequencies of the three tones in the original train whistle signal?
What is the carrier frequency of the modulator signal?
Are the baseband tones identifiable in the modulated signal?
Experiment with the value of the modulation index (line 31 of the code) and rerun the program for various values. What do you observe?

function fm_example
%download built in MATLAB sound file of a train whistle
load train
%play the sound through the speakers
y=y';
soundsc(y, Fs)
%Set up plotting parameters
dt=1/Fs;
N=length(y);
t=(0:(N-1))*dt;
%examine the spectrum of the signal
plot_fft_spectrum(t, y,1);
%upsample the signal Y to 128K samples per second
y128=interp(y,16);
Fs128=Fs*16;
dt128=1/Fs128;
N128=N*16;
t128=(0:(N128-1))*dt128;
%replay and re-examine the spectrum of the signal
soundsc(y128,Fs128)
plot_fft_spectrum(t128,y128,2);
%now modulate to a carrier using dsb_sc
fc=16384; %carrier frequency
kk=8000; %maximum frequency deviation
ymod = cos(2*pi*fc*t128 + 2*pi*kk*cumsum(y128)*dt128);
%examine the spectrum of the modulated signal
plot_fft_spectrum(t128,ymod,3);
%fm demodulate the signal
yq = hilbert(ymod).*exp(-j*2*pi*fc*t128) ;
ydemod = (1/(2*pi*kk))*[0 diff(unwrap(angle(yq)))*Fs128];
soundsc(ydemod, Fs128)
plot_fft_spectrum(t128,ydemod,5); dum=1;