I am looking for a treatment of fundamental DSP theory where only discrete/finite signal models are used. To make a concrete example, every time standard textbooks write a convolution as a continuous integral, I would like to see instead a product between a Toeplitz matrix and a vector. It seems to me that developing such a theory from linear algebra would make implementing concrete DSP algorithm much easier. Think also of multirate/filter banks, etc... Except maybe for the book of Strang on Wavelets I have not seen any other book based this approach. Any book titles I have missed?
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