Notes on Linear Systems and Impulse Responses

We show that the members of a certain important large family of multidimensional linear systems are completely characterized by their (suitably defined) impulse responses—which we show exist as certain limits. Not all linear shift-invariant systems are characterized by their impulse responses. Our results contribute to the reconstruction of an important part of the engineering theory of linear systems that had been based on the flawed concept of the Dirac impulse function.