Question

Exercise 2.5 response of the LTI system with impulse response h(t)-e cos(2t)u(t)

Answer 1

To find the step response we have to transfer from time domain to Laplace domain..again by transforming from Laplace domain to time domain we will get step response..step response means the output response when input is step signal..the impulse response means the output response when input is impulse signal
Given h (t) = e^- t cos (2 t) u (t) step(1): step response rightarrow input = step input where, h (t) = impulse response u (t) = input signal y (t) = output response = step response step(2): applying Laplace transforms rightarrow y (s) = (s + 1)/(s + 1)^2 . 1/s = (s + 1)/s [s^2 + 2s + 1 + 4] y (s) = s + 1/s (s^2 + 2s + 5) using practical fractions s + 1/s (s^2 + 2s + s) = a/s + bs + c/s^2 + 2 s + 5