# step and impulse response of a system

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SSBGH on 13 Nov 2022
Answered: Bhavana Ravirala on 16 Nov 2022
i have a question which is the following:
impulse respone of a system is h(t) =( exp(-0.05*t) )
Excitation of a system is x(t) = u(t)*cos(2*pi*t)
1-in subplot 1 show the impulse respone of the system
2-in subplot 2 show the Excitation of the system
3-in subplot 3 show the response of the system
4-in subplot 4 show the step response of the system
where t range is from 0...100
code:
t = 0:100;
u = heaviside(t);
impulse = [];
excitation = [];
for i =1:numel(t)
impulse(i)= exp(-0.05*t(i));
end
for i =1:numel(t)
excitation(i) = u(i).*cos(2.*pi.*t(i));
end
subplot(2,2,1)
plot(t,impulse)
title('impulse response')
subplot(2,2,2)
plot(t,excitation)
title('excitation')
c = conv(excitation,impulse,"same");
subplot(2,2,3)
plot(t,c)
title("Response")
step = conv(u,impulse,"same");
subplot(2,2,4)
plot(t, step)
title("Step Response")
i'm not sure that the solution is correct because i'm getting the response of the system and step response figure both the same, so any ideas whether the solution is good or no?

Bhavana Ravirala on 16 Nov 2022
As the range of ‘t’ is from 0 to 100 you can use “linspace” command. By using these ‘t’ values we will get proper cos signal. And for loops are not required to generate impulse and excitation signals.
t=linspace(0,100);
u=heaviside(t);
excitation=u.*cos(2*pi.*t);
impulse=exp(-0.05*t);
subplot(2,2,1)
plot(t,impulse)
title('impulse response')
subplot(2,2,2)
plot(t,excitation)
title('excitation')
c = conv(excitation,impulse,"same");
subplot(2,2,3)
plot(t,c)
title("Response")
step = conv(u,impulse,"same");
subplot(2,2,4)
plot(t, step)
title("Step Response") 