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Analysis of LTI-systems and complete characterization of systems of the convolution type
In this paper, the behaviour of discrete-time SISO-stable linear systems is investigated. The main idea of the theory of a discrete-time single-input single-output linear system is that every such system has an input-output map that can be represented by the well known convolution sum. These systems are called systems of the convolution type. It was recently discovered by Boyd and Sandberg that not all discrete-time single-input single-output linear systems are systems of the convolution type. Hence it would be interesting to characterize the systems of the convolution type. Such a characterization is given in the paper. FIR-systems are also investigated.