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Definition and explanation of the unt step function, used in electronics applications. Trench via source content that was edited to the style and standards of the libretexts platform. We learn how to find laplace transforms of unit step functions Includes the time displacement theorem. A unit impulse adds a total of 1 unit in one instant If the impulse is at t = t0 then all the input happens at t = t0 An impulse as the limit of a sequence of boxes as they get narrower and taller The unit step function u(t) is sometimes called the heaviside function It can be denoted h(t) (heaviside in matlab), and sometimes other symbols like (t). Just as with the unit step function, the graph has ‘infinite’ slope at a jump and the integral of the derivative should give the original function This is exactly what functions do at jumps. A unit step function is a mathematical function that switches on at time t=0 and is represented by the values 1 for t≥0 and 0 for t<0 It is commonly used in computer science to represent an idealized switch and can be multiplied by other functions to switch them on at t=0. There is only one unit step function, , u (t), in the same way that there is only one sine function, sin (t) We will now build on the definition to learn more about how this function behaves. 3.2 unit step function • in many circuits, waveforms are applied at specified intervals other than at t = 0 Such a function may be described using the shifted unit step function. Unit step function and representation of functions with jumps Represents a jump of unit size at t = 0 Represents a jump of unit size at t = a Note that u(t − a) is sometimes denoted by ua(t) Represents a jump of size m at t = a Therefore a “jump” of any size at anywhere can be thus represented Where g(t) is a nice function.