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The convolution integral provides a solution to the inverse transform of the product of functions of s: \({\mathcal {L}}^{-1}(F_1(s)F_2(s)) = f_1(t)*f_2(t)\) . This provides an interpretation to memory in dynamical systems, in which the present value of the output \(v_{out}(t)\) depends not only on the present value of the input \(v_{in}(t)\) but also on the past history of the input. In particular, the convolution integral shows that the circuit output is the weighted average of the past history of the input signal, weighted through the circuit impulse response.

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Convolution

  • 章节

  • 发表日期：

    2026年

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  • Robert W. Erickson

摘要

The convolution integral provides a solution to the inverse transform of the product of functions of s: \({\mathcal {L}}^{-1}(F_1(s)F_2(s)) = f_1(t)*f_2(t)\) . This provides an interpretation to memory in dynamical systems, in which the present value of the output \(v_{out}(t)\) depends not only on the present value of the input \(v_{in}(t)\) but also on the past history of the input. In particular, the convolution integral shows that the circuit output is the weighted average of the past history of the input signal, weighted through the circuit impulse response.