signals and systems

*** show all answers and do all parts

Chirps-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

clear all;clf

t=0:0.05:40;

% chirps

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

y1=cos(2*t- 2*sin(t));

figure(14)

subplot(211)

plot(t,y); title(linear chirp)

axis([0 20 1.1*min(y) 1.1*max(y)]);grid

subplot(212)

plot(t,y1);title(sinusoidal chirp);xlabel(t)

axis([0 20 1.1*min(y1) 1.1*max(y1)]);grid

% instantaneous frequencies

IF=2+2*t/4;

IF1=2-2*cos(2*t);

figure(15)

subplot(211)

plot(t,IF);title(IF of linear chirp)

ylabel(frequency); xlabel(t);grid

subplot(212)

plot(t,IF1);title(IF of sinusoidal chirp)

ylabel(frequency);xlabel(t);grid

y(t) A cos(S2ct s(t)) Let A 1, S2 2, and s(r) use MATLAB to plot this signal for o in steps 2/4. listen to the s sec of 0.05 sec. use sound to t s 40 signal. Let A 1, S2 2, and s(t) 2 sin(t) use MATLAB to plot this (b) signal for 0 t s 40 sec in steps of 0.05 sec. use sound to listen to the signal. (c) What is the frequency of a chirp? It is not clear. The instanta- neous frequency IF(t) is the derivative with respect to t of the argument of the cosine. For instance, for a cosine cos(2ot) the so so that the instantaneous frequency coin cides with the conventional frequency. Determine the instanta neous frequencies of the two chirps and plot them. Do they make sense as frequencies? Explain