(a) Using MATLAB and a sampling frequency of fs=14000 Hz. with a corresponding s

Question

(a)

Using MATLAB and a sampling frequency of fs=14000 Hz. with a corresponding sampling interval of Ts=1/fs, generate a vector of times from 0 3 sec. using the MATLAB command

>> t=0:Ts:3;

Create a signal x1 that is 3 seconds long consisting of a 3000 Hz sinusoid in the interval [0, 1], a chirp going from 3000 to 6000 Hz in the interval [1, 2], and the a 6000 Hz signal in the interval [2, 3].

(b)

Use the MATLAB spectrogram function to plot the time-varying spectrum of the x_1 signal generated in part(a) above.

Explanation / Answer

clc;
close all;
clear all;

Fs = 14000;
Ts = 1/Fs;
t = 0:Ts:3; %sampling window length

SIG = []; %array to concatenate data

for i = 1 : 1 : 3;
    if i == 1
        tx = 0:Ts:1-Ts;
        xt1 = sin(2*pi*3000*tx); %FIRST 1 SECOND
        figure(1);
        plot(tx,xt1); %EACH INDIVIDUAL PLOT
      
    elseif i == 2
        tx= 0:Ts:1-Ts;                   
        fo=3000;f1=6000;                   
        xt1=chirp(tx,fo,1,f1,'q',[],'convex'); %SECOND 1 SECOND
        figure(2);
        plot(tx,xt1); %EACH INDIVIDUAL PLOT
      
    else
        tx = 0:Ts:1;
        xt1 = sin(2*pi*6000*tx); %THIRD 1 SECOND
        figure(3);
        plot(tx,xt1); %EACH INDIVIDUAL PLOT
      
    end
    SIG = [SIG,xt1];
end
figure(4);
subplot(2,1,1);
plot(t,SIG);        %PLOT OF SIGNAL
title('SIGNAL');

subplot(2,1,2);
[S,F,T] = spectrogram(SIG,200,3,10,14000); %OUTPUT DATA
plot(T,S);        %PLOT OF SPECTRUM
title('SPECTRUM');

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