Matrix Representation of Linear Systems Relationships

We defined the eigenvalues of the circulant matrix using the first row of Hp, i.e. hp(-j). Thus the diagonal elements are:

Since hp is periodic, summation from 0 to -(N-1) is equal to summation from 0 to (N-1). Thus -j may be replace by j:

Let the DFT of hp(j) be

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