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论文期刊

论文标题    The Superposition Principle of Linear Time-Invariant Systems
作者    Ming Zhang and Anxue Zhang
发表/完成日期    2019-11-15
期刊名称    IEEE Signal Processing Magazine
期卷    36 (6)
相关文章   
论文简介    It is well known that the output signal of a linear time-invariant (LTI) system can be expressed as the convolution of the input signal and the system's impulse response. However, the derivation of this result is not rigorous in the majority of the literature. Because a linear operator defined on an infinite-dimensional space may be discontinuous, the order of the linear operator and the summation cannot be interchanged arbitrarily. Therefore, the superposition principle of LTI systems is only valid for finitely many terms, but not for infinitely many terms. In this note we prove that a necessary and sufficient condition for the superposition principle with infinitely many terms is that the system is linear and continuous.
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