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transfer function is laplace transform of impulse response of LTI system ....so if we give unit step input to a lti system,would it not have transfer function?
That's correct, the trasnfer function of a continuous-time system is the Laplace transform of its impulse response. If we put a unit step into an any LTI system, we call the resulting output the step response of the system. The step response of the system and the impulse response of the system are related to each other. If we have the step response of the system we can obtain the impulse response by taking the derivative of the step response. Once we have the impulse response, then we could take the Laplace transform to get the transfer function. Hope that helps, Adam