On the Eigenvalues of Matrices for the Reconstruction of Missing Uniform Samples

In this correspondence, we derive the relationship between the eigenvalues associated with the matrices of the minimum dimension time-domain and frequency-domain approaches used for reconstructing missing uniform samples. The dependency of the eigenvalues of the weighted Toeplitz matrix on positive weights are explored. Simple bounds for the maximum and minimum eigenvalues of the weighted Toeplitz matrix are also presented. Alternative matrices possessing the same nonzero eigenvalues as that of the weighted Toeplitz matrix are provided. We verify the theory by the examples presented.