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8: Pulse Inputs; Dirac Delta Function; Impulse Response; Initial Value Theorem; Convolution Sum

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  • We analyzed previously the response of systems to a half-sine pulse input (e.g., in Sections 1.5 and 1.6). In this chapter, we will continue analysis of pulse excitation and subsequent dynamic response. Most importantly, we will extend the analysis to the concept of the impulse, which in its simplest form is \(u \times t_{d_{d}}\), the product of excitation and the duration of excitation. In particular, the Dirac delta or ideal unit-impulse function is essential in the theory of linear systems and also useful in practical applications.