Lab sheet -4


Signals and System




  1. Write a Matlab code for sampling following signal.

    x (t) =sin (2πF1t) + sin (2πF2t)

    Take the time range t= [0:0.1:20]

    F1=0.1 and F2=0.2

Code:

Xlabel (‘n’);

Ylabel (‘x_samples’);

Title (‘Sample’);

x_recon=0;

subplot (3,1,3);

for k=0:length(x_samples)-1

stem (0:length(x_samples)-1,x_samples);

l=k:-.1:-20+k;

x_recon=x_recon+x_samples(k+1)*sinc(l);

axis ([0 20 -2 2]);

hold ;

plot (t,x_recon,’ko’);

end;

xlabel(‘t’);

ylabel (‘x_recon’);

title (‘Reconstructed Signal’);

Figure:

  1. Find DTFT for given specifications

    Num= [1 -0.6]

    Den= [2 1]

    Plot magnitude spectrum and phase spectrum.

Code:

Num = [1 -.6];

Den = [2 1];

w= -4*pi:8*pi/512:4*pi;

h=freqz (num,den,w);

subplot (2,2,1);

plot (real(h),’k.’);

title (‘Plot of real(h)’);

SUBPLOT (2,2,2);

Plot (imag(h),’ko’);

Title (‘Plot of Imag(h)’);

Subplot (2,2,3);

Plot (angle(h),’kx’);

Title (‘Plot of phase spectrum’);

Subplot (2,2,4);

Plot (abs(h),’k-‘);

Title (‘Plot of magnitude spectrum’);

Figure:

  1. Write a Matlab code for finding CTFT of following signal.
    1. x(t)=2cos(10πt)
    2. x(t)=ce5t

      Plot magnitude spectrum and phase spectrum.

      b. Code:

t=0:0.01:2;

c=2;

x=c* exp (5*t);

N=100;

y=fft(x,N);

subplot (3,1,1);

plot (t,x,’k*’);

title (‘Given Signal x(t)=2cos(10*pi*t)’);

subplot (3,1,2);

plot (abs(y),’ks’);

title (‘Plot of abs(y)’);

subplot (3,1,3);

plot (angle(y),’kd’);

title (‘Plot of angle(y)’);

  1. Figure:


  1. Code:

t=0:0.01:2;

x=2*cos(10*pi*t);

N=100;

y=fft(x,N);

subplot (3,1,1);

plot (t,x,’kp’);

grid;

title (‘Given Signal x(t)=2cos(10*pi*t)’);

subplot (3,1,2);

plot (abs(y),’k’);

grid;

title (‘Plot of abs(y)’);

subplot (3,1,3);

plot (angle(y),’k:’);

grid;

title (‘Plot of angle(y)’);

 

  1. Figure:

     

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