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Closed-Form Impulse Responses of Linear Time-Invariant Systems: A Unifying Approach

In many signal processing applications, filtering is accomplished through linear time-invariant (LTI) systems described by linear constant-coefficient differential and difference equations since they are conveniently implemented using either analog or digital hardware [1]. An LTI system can be completely characterized in the time domain by its impulse response or in the frequency domain by its frequency response, which is the Fourier transform of the system’s impulse response.

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