Solution to convolution integral of the product of two continuous functions, for example, \(x(t) h(t)\) , is a third function of the same variable, e.g., \(f(t)\) . In this chapter, various combinations of the integrals that include special functions (distributions) are solved in detail. The “integral” implies that functions being convoluted are continuous (including quasi-continuous special functions), that is to say, non-sampled. In addition, typical problems related to energy and power of continuous functions are solved.

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Continuous Time Convolution

  • Robert Sobot

摘要

Solution to convolution integral of the product of two continuous functions, for example, \(x(t) h(t)\) , is a third function of the same variable, e.g., \(f(t)\) . In this chapter, various combinations of the integrals that include special functions (distributions) are solved in detail. The “integral” implies that functions being convoluted are continuous (including quasi-continuous special functions), that is to say, non-sampled. In addition, typical problems related to energy and power of continuous functions are solved.