Question

Task 3 Generate the following signals and classify them as periodic or aperiodic. State reasons. (4.5 marks) -3t 1) x(t) = 3e 2) X(t) = 573 sin(51) + cos cos (§ 1) 3) X(t) = 4e+24+ cos cos (++)

solve using scilab
show the codes

Answer 1

Task 3

1.

3 2.5 3 1.5 1 - 0.5 0 T T 0 0.2 0.4 0.6 0.8 1.2 1.4 1 1.6 1.8 2 t

1 clear; 2 clc; 3 t =0:0.01:2; 4 x = 3*exp(-3*t); 5 subplot(2,1,1); 6 plot(t, x); 7 xlabel('t'); 8 ylabel('x(t)'); 9 ylabell

This is an aperiodic signal.

2.

sinewave 1 sinewave 2 resultant wave 10 3.6 12 8 3.4 10 6 8 3.2 - 4 6 3- 2 4 2.8 x1 (t) 0 x2 (t) X(t) 2 2.6 - -2 0 2.4 - -4 -2 2.2 -6 -4 -8 2 -6 -10 1.8 -8 0 10 20 30 0 10 20 30 0 10 20 30 t t t

1 clc ; 2 clf ; 3 // clear all; 4 t =0:0.1:30 5 x1 = 5*sqrt(3)*sin ( %pi * t /3); 6 z = 5/sqrt(2); 7 u = cos(%pi * t /2); 8 x2 = z* cos(u) ; 9 x = x1 + x2 ; 10 11 subplot (1,3,1); 12 plot (t, x1 ) ; 13 title ( 'si new av e 1' ); 14 xlabel ('t'); 15 ylabel ( ' x1 ( t)'); 16 17 subplot (1,3,2) ; 18 plot (t, x2 ); 19 title ( 'si newave 2' ); 20 xlabel ('t'); 21 ylabel ('X2 ( t ) X2 ( t)'); 22 23 subplot (1,3,3) ; 24 plot (t, x); 25 title ( 'resultant wave' ); 26 xlabel ( 't'); 27 ylabel ('x ( t)');

This is a periodic signal

3.

exponential function cos function resultant function 4 1.9 5.5 1.8 5 in 1.7 4.5 - 3 1.6 4 - 2.5 1.5 3.5 1 x2(t) 2 x1 (t) x(t) 1.4 3- 1.5 1.3 2.5 - 1.2 2 0.5 1.1 1.5 - M 0 1 1 0 5 15 20 0 5 10 15 20 0 5 10 15 15 20 10 t t t

1 clc ; 2 clf ; 3 //clear all; 4 t =0:0.01:20; 5 6 7 z = 5/sqrt(7); 8 u = cos(%pi * t /4); 9 x1 = z*cos(u); 10 11 X2 = 4*exp(-2*t) ; 12 x = x1 + x2 ; 13 14 15 16 subplot (1,3,1); 17 plot (t, x2 ); 18 title ( 'exponential function' ); 19 xlabel ('t'); 20 ylabel('x2(t)'); 21 22 subplot (1,3,2); 23 plot (t , x1 ); 24 title ( 'cos function' ); 25 xlabel ('t'); 26 ylabel('x1(t)'); 27 28 subplot (1,3,3); 29 plot (t x); 30 title ( 'resultant function'); 31 xlabel ('t'); 32 ylabel('x(t)');

This is an aperiodic signal