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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 impulse response and step response are transient responses to a specific input (an impulse and a step, respectively). In electrical engineering specifically, the transient response is the circuit’s temporary response that will die out with time. [1]
The impulse response of a linear transformation is the image of Dirac's delta function under the transformation, analogous to the fundamental solution of a partial differential operator. It is usually easier to analyze systems using transfer functions as opposed to impulse responses. The transfer function is the Laplace transform of the impulse ...
In other words, a very small change in stimulus causes a very large change in response, producing a sigmoidal dose-response curve. An ultrasensitive response is described by the general equation V = S n /(S n + K m), known as the Hill equation, when n, the Hill coefficient, is more than 1. The steepness of the sigmoidal curve depends on the ...
External stimuli are capable of producing systemic responses throughout the body, as in the fight-or-flight response. In order for a stimulus to be detected with high probability, its level of strength must exceed the absolute threshold ; if a signal does reach threshold, the information is transmitted to the central nervous system (CNS), where ...
In response, model based on signal-dependent noise was proposed instead, which states that the CNS selects a trajectory by minimizing the variance of the final position of the limb endpoint. Since there is a motor noise in the neural system that is proportional to the activation of the muscles, the faster movements induce more motor noise and ...
The impulse response function provides that factor as a function of the elapsed time since each input value occurred. In physics , wherever there is a linear system with a " superposition principle ", a convolution operation makes an appearance.
The step response can be interpreted as the convolution with the impulse response, which is a sinc function. The overshoot and undershoot can be understood in this way: kernels are generally normalized to have integral 1, so they send constant functions to constant functions – otherwise they have gain.