Computing and the Step Function

One aspect of the engineering education that the author began back in the early 1950\´s seemed very strange at the time. It was the serious consideration of the step function, which was unlike anything treated in highschool mathermatics because it was discontinuous. While its relevance to the design of mechanical and electrical machinery soon became obvious, it has recently occurred to the author that the step function is just as relevant to the use of machinery, in particular, computers. The engineering problem is that x is usually a value of time, thus the step function requires an instantaneous change from y\´ to y". In spatial terms, this is an indefinitely large acceleration. In mechanical terms, it means an indefinitely large force. These are unnatural and, in physical systems at least, neither an input nor an output can be exactly stepped. The engineering challenge is to take an input that\´s practically a step function and give an output that can be used as a step function, sometimes after cleaning it up. In digital circuitry, the square waves that encode bits in transmission are ideally a sequence of step functions, and the bit rate is limited by the distortion during transmission.