TY - JOUR

T1 - An inverse problem for Toeplitz matrices and the synthesis of discrete transmission lines

AU - Caflisch, Russel E.

N1 - Funding Information:
*Most of this work was performed at Bell Telephone Laboratories, Murray Hill, NJ 07974. Additional support was provided by the National Science Foundation.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1981/6

Y1 - 1981/6

N2 - Let Am be a positive definite, m x m, Toeplitz matrix. Let Ak be its k x k principal minor (for any k≤m), which is also positive definite and Toeplitz. Define the central mass sequence {ρ{variant}1,...,ρ{variant}m} by ρ{variant}k = sup{ρ{variant}: Ak - ρ{variant}Πk > 0}, in which Πk is the k x k matrix of all 1's. We show how knowledge of the sequence {ρ{variant}k} is equivalent to knowledge of the matrix Am. This result has application to the direct and inverse problems for a transmission line which consists of piecewise constant components. Knowing the impulse response of the transmission line, we can calculate the capacitance taper of the line, and vice versa.

AB - Let Am be a positive definite, m x m, Toeplitz matrix. Let Ak be its k x k principal minor (for any k≤m), which is also positive definite and Toeplitz. Define the central mass sequence {ρ{variant}1,...,ρ{variant}m} by ρ{variant}k = sup{ρ{variant}: Ak - ρ{variant}Πk > 0}, in which Πk is the k x k matrix of all 1's. We show how knowledge of the sequence {ρ{variant}k} is equivalent to knowledge of the matrix Am. This result has application to the direct and inverse problems for a transmission line which consists of piecewise constant components. Knowing the impulse response of the transmission line, we can calculate the capacitance taper of the line, and vice versa.

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U2 - 10.1016/0024-3795(81)90021-5

DO - 10.1016/0024-3795(81)90021-5

M3 - Article

AN - SCOPUS:33748330056

VL - 38

SP - 207

EP - 225

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - C

ER -