Pure tones or sinusoids are not very interesting to listen to. Modulation and ot

Question

Pure tones or sinusoids are not very interesting to listen to. Modulation and other techniques are used to generate more interesting sounds. Chirps, which are sinusoids with time-varying frequency, are some of those more interesting sounds. For instance, the following is a chirp signal: y(t) = A cos( Ohm ct + s(t)) Let A = 1. Ohm c = 2, and s(t) = f2/4. Use MATLAB to plot this signal for 0 t 40 sec in steps of 0.05 sec. Use the sound function to listen to the signal. Let A = l. Ohm c = 2. and s(t) = -2 sin(t). Use MATLAB to plot this signal for 0 t 40 sec in steps of 0.05 sec. Use the sound function to listen to the signal. The frequency of these chirps is not clear. The instantaneous frequency IF(t) is the derivative with respect to t of the argument of the cosine. For instance for a cosine cos( Ohm 0t), the IF(t) = d Ohm 0t/dt = Ohm 0, so that the instantaneous frequency coincides with the conventional frequency. Determine the instantaneous frequencies of the two chirps and plot them. Do they make sense as frequencies? Explain.

Explanation / Answer

a=1;

w=2;

t=0:0.05:40;

y=a*cos(w*t+(t.^2/4));

plot(t,y)

sound(y);

a=1;

w=2;

t=0:0.05:40;

y=a*cos(w*t-2*sin(t));

plot(t,y)

sound(y);

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