(a) Using the convolution integral, prove that if the response of an LTI system to r(t)…

(a) Using the convolution integral, prove that if the response of an LTI system to r(t) is the output y(t), then the response of the system to input 1. dx(t) () dt is /(t)=0 (b) A linear time-invariant system produces output y(t) (1-e)ut) in response to the input u(t), where u(t) is the unit step function. dt i. Find the impulse response of the system. i. Find the system response when the input is the ramp function r(t) = tu(t)