A New Systolic Design for Digital HR Filters
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چکیده
In this letter we have considered convolution from an algebraic standpoint and presented several examples that may be of interest to the engineering community. In particular, we showed that convolution need not be associative. This result, among other things, should cause some concern in the analysis of cascaded systems. Further, we showed that convolution of nowhere zero bounded integrable functions could be everywhere zero. This result should be of some interest to those attempting to identify the input to a linear time-invariant system via some operations on the output, such as in deconvolution problems. Further, this result again shows a problem that may arise in the analysis of cascaded systems in that two linear time-invariant systems each characterized by convolution with a nowhere zero function can, when cascaded, result in a no-pass filter.
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