How to find output of system with impulse response function

How i can find the output of system with impulse response function h(t) = sin(t) u(t) for input f(t) = exp(-t)u(t) in MATLAB?

Answer 1

[Bhavana Ravirala]

Hi Mandeep,

From my understanding you are trying to find output of the system which can be obtained by convolution of input and impulse response. The convolution can be obtained by product of Laplace transform of both the signals.

syms t;   % t is a variable 
impulseResponce=exp(-t); 
input=sin(t); 
k=laplace(impulseResponse)*laplace(input);   % product of laplace transforms
output=ilaplace(k);   % inverse laplace transform 

For more information refer to the documentations below:

Create symbolic scalar variables, functions, and matrix variables - MATLAB syms (mathworks.com)

Laplace transform - MATLAB laplace (mathworks.com)

Inverse Laplace transform - MATLAB ilaplace (mathworks.com)

Hope this helps.