A chirp signal is defined in MATLAB as t 081928192 x cos81

A chirp signal is defined in MATLAB as

t = [0:8192]/8192;
x = cos(8192*pi*t.*t);

It is convolved with 12-point real-valued filter whose magnitude discrete-time Fourier transform (DTFT) is shown below. Sketch the envelope of the output of the convolution; label axes carefully. Explain.

0) Discrete Frequency,uw(rad)

Solution

clear all;

close all;

x=input(\'enter the sequence\');

subplot(3,1,1);

stem(x);

xlabel(\'time\');

ylabel(\'magnitude\');

title(\'input sequence\');

N=length(x);

y=(zeros(1,N));

x=bitrevorder(x);

q=1;

for m=1:1:(log(N)/log(2))

for n=1:1:N/2^m

for p= 1:1:2^(m-1)

            a=x(q);

            b=x(q+2^(m-1));

            y(q)=a+b;

            y(q+2^(m-1))=(a-b)*exp(-i*2*pi*(p-1)/2^m);

            q=q+1;

end

       q=2*m*n+1;

end

    q=1;

for t=1:1:N

        x(t)=y(t);

end

end

y=bitrevorder(x);

subplot(3,1,2);

stem(abs(y));

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'magnitude\');

subplot(3,1,3);

stem(angle(y));

xlabel(\'angle\');

ylabel(\'amplitude\');

title(\'angle of DIF-FFT\');

disp(y);

gtext(\'kluniversity\')