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

• Published in: IEEE transactions on signal processing Vol. 58; no. 5; pp. 2896 - 2900
• Main Authors: Karthik, M, Prabhu, K M M
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: ACT algorithm; adaptive weights; Applied sciences; Digital signal processing; Discrete Fourier transforms; Eigenvalues; Eigenvalues and eigenfunctions; Equations; Exact sciences and technology; Extrapolation; Information, signal and communications theory; Interpolation; Mathematical analysis; Matrices; Matrix methods; minimum dimension time-domain and frequency-domain approaches; Miscellaneous; optimal weights; Reconstruction; Signal processing; Signal processing algorithms; Signal sampling; Telecommunications and information theory; Time domain analysis; weighted Toeplitz matrix; Minimum time; Time frequency domain method; weighted Toeplitz matrix; minimum dimension time-domain and frequency-domain approaches; Signal processing; Eigenvalue; adaptive weights; optimal weights; Toeplitz matrix; Algorithm; ACT algorithm
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2041277

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.