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Determination of the steady-state behaviour of the state variables of a second-order filter with syllabic companding

In order to get a better understanding on the concepts of dynamic eigenvalues and dynamic eigenvectors as presented in [1], the steadystate behaviour of the state variables of the filter with syllabic companding described in [2] is determined. For that purpose, the approach presented in [3] is used. Some comments are made regarding the general form of the solution of the Riccati equation involved in the procedure described in [3] and it is proven that the selection of the initial condition required for determining a valid solution which could be used to determine the exact dynamics of the filter is not arbitrary. Besides the computations of the steady-state response of the state variables, the determination of the Floquet exponents assuming that the state equations of the filter are periodic support the hypothesis stated above. Keywords— Syllabic companding, dynamic eigenvalues, dynamic eigenvectors, Riccati equation, Lyapunov transformations, Floquet exponents.