ABSTRACT
For positive integers k and n, the n × n $ n\times n $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/inline-math4_1.tif"/> k-Circulant matrix with the input sequence { x k } $ \{x_k\} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/inline-math4_2.tif"/> , is defined as A k , n = x 0 x 1 x 2 … x n - 2 x n - 1 x n - k x n - k + 1 x n - k + 2 … x n - k - 2 x n - k - 1 x n - 2 k x n - 2 k + 1 x n - 2 k + 2 … x n - 2 k - 2 x n - 2 k - 1 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ x k x k + 1 x k + 2 … x k - 2 x k - 1 n × n . $$ A_{k,n} \ = \left[ \begin{array} {cccccc} x_{0}&x_{1}&x_{2}&\ldots&x_{n-2}&x_{n-1} \\ x_{n-k}&x_{n-k+1}&x_{n-k+2}&\ldots&x_{n-k-2}&x_{n-k-1} \\ x_{n-2k}&x_{n-2k+1}&x_{n-2k+2}&\ldots&x_{n-2k-2}&x_{n-2k-1} \\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots \\ x_k&x_{k+1}&x_{k+2}&\ldots&x_{k-2}&x_{k-1}\\ \end{array} \right]_{n\times n}. $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/unmath4_1.tif"/>
