Question

please, provide answer along with its matlab code.

10. Consider the continuous- time signal kite a1ua(-t) + kze-a2t cos (2mfi t) ua (t), Ta(t) where ki =-400, k2 2, a1 = -57.5364, a2 21.0721, and fi=300 Hz. (a) Plot ra(t). Identify the non-causal part of Ta (t) as Tal(t) and the causal part as Ta2(t). (b) Assuming that aa(t) is sampled using the sampling frequency fsamp 200 Hz, determine the discrete-time counter-parts corresponding to aal (t) and ra2(t), named a1(n) and 2(n), respectively. Hence, plot r(n). (c) Determine the energy of the entire signal.

Answer 1

MATLAB code for the given problem:

clc;clear all;close all;
%continous time signal xa(t)
k1=-400;k2=2;a1=-57.5364;a2=21.0721;f1=300;T=10*(1/f1);
t=-T:T/500:T
xa=((k1*t.*(exp(-a1*t))).*(t<=0))+(k2*(exp(-a2*t)).*(cos(2*pi*f1*t)).*(t>=0))

subplot(321)
plot(t,xa,'b');xlabel('t');ylabel('xa(t)');title('xa(t)')

%non causal part of xa(t)
xa1=xa.*(t<0)
subplot(322)
plot(t,xa1,'r');xlabel('n');ylabel('xa1(t)');title('xa1(t)')
%causal part of xa(t)
xa2=xa.*(t>=0)
subplot(323)
plot(t,xa2,'m');xlabel('n');ylabel('xa2(t)');title('xa2(t)')

fsamp=200;Ts=1/fsamp;
n=-T*fsamp:1:T*fsamp
t=n/fsamp;
%sampled signal x(n) and x2(n)
x=((k1*(n/fsamp).*(exp(-a1*n/fsamp))).*(n<0))+(k2*(exp(-a2*n/fsamp)).*(cos(2*pi*f1*n/fsamp)).*(n>=0))
x1=x.*(n<0)
x2=x.*(n>=0)

subplot(324)
stem(n,x1,'b');xlabel('n');ylabel('x1(n)');title('x1(n)')

subplot(325)
stem(n,x2,'m');xlabel('n');ylabel('x2(n)');title('x2(n)')

subplot(326)
stem(n,x,'r');xlabel('n');ylabel('x(n)');title('x(n)')

%Enery of the entire signal
E=sum((abs(x)).*2)

Plots:

ха1(t) ха(t) 3 2.5 2 2 1 1.5 1 0,5 1 0 2 0.04 0.02 -0.02 0.04 0.04 0.02 0.02 -0.04 n х1(n) ха2(t) 2 2,5 2 1,5 1 0.5 ө00өөөю- 10 2 0 -5 10 0.04 0.02 -0.02 -0.04 n n x(п) x2(n) 3 2 1 0 1 -2 -2 10 5 10 10 5 -10 n n LO mnan (u)x (1) Lex (u) LX O C N O xa2(t) x2(n)

Command window:

E = 49.771