Time Convolution with the Unit Step Response

Abstract

Similar to the impulse response we can use the unit step input to characterize systems/circuits and obtain what is referred to as the unit step response. Once we know this we can now apply any other input and simply convolve the derivative of that input with the unit step response. Notice we convolved the derivative of the input, as opposed to the input itself was is normally done when using the impulse response. We start the chapter by reviewing how the unit step function can be used to generate an arbitrary signal. Then and as a test vehicle we use the low-pass filter circuit and use its step response to figure the response to other stimuli, such as the periodic pulse, periodic triangle, the ramp input, and the causal sine one. The process of building the solution in terms of scaled, offset unit step ones is illustrated in detail, and visually throughout the examples.