Consider a discrete time LTI system with impulse response given by: h[n] = u[n +
ID: 3076419 • Letter: C
Question
Consider a discrete time LTI system with impulse response given by: h[n] = u[n +2] - 2u[n-1] + u[n - 4].
Sketch the impulse response h[n], then sketch the step response ys[n]
Explanation / Answer
its u(t-1)-u(t-3)......................using convolution : h(t) * u(t) |........ _______ |_____|______|____________>t .........1......... 3 To obtain a step response you multiply the closed loop transfer function by 1/s and anti transform, in the same way you did with the pulse response. The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter
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