Cepstral coefficients, covariance lags, and pole-zero models for finite data strings

Ryrnes, C.I.; Enqvist, Per; Lindquist, Anders

doi:10.1109/78.912912

Cited by 59 publications

(65 citation statements)

References 26 publications

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“…This generalizes classical cepstrum theory [7,8] to the time-varying case. We also discuss the relation of the CTFC with the evolutionary cepstrum introduced in [2].…”

Section: Tf Cepstrum and Tf Cepstral Recursionsupporting

confidence: 62%

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Time-frequency-moving-average processes: principles and cepstral methods for parameter estimation

Jachan

Matz

Hlawatsch

2004 IEEE International Conference on Acoustics, Speech, and Signal Processing

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We introduce the time-frequency-moving-average (TFMA) model as a highly parsimonious time-varying MA model formulated in terms of time-frequency (TF) shifts. For estimation of the TFMA model parameters, we develop a computationally efficient nonlinear technique based on a novel complex TF cepstrum, TF cepstral recursions, and an underspread approximation. Simulation results demonstrate significant performance advantages of the proposed TFMA model and parameter estimation technique over an existing method for time-varying MA modeling and estimation.

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“…This generalizes classical cepstrum theory [7,8] to the time-varying case. We also discuss the relation of the CTFC with the evolutionary cepstrum introduced in [2].…”

Section: Tf Cepstrum and Tf Cepstral Recursionsupporting

confidence: 62%

“…[7]). If the system is time-invariant, then S[m, l] = 0 for l = 0 and thus the CTFC reduces to the classical complex cepstrum [7,8].…”

Section: The Complex Tf Cepstrummentioning

confidence: 99%

Time-frequency-moving-average processes: principles and cepstral methods for parameter estimation

Jachan

Matz

Hlawatsch

2004 IEEE International Conference on Acoustics, Speech, and Signal Processing

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“…In the scalar case = 1, it was noted in [4,5] that the entropy gain (4.1) is precisely the zeroth cepstral coefficient c 0 and that the cepstral coefficients (4.2) together with the covariance data W form local coordinates of F + (n). This observation led to maximizing linear combinations of the cepstral coefficients instead.…”

Section: Main Theoremsmentioning

confidence: 99%

“…Applications of Nevanlinna-Pick interpolation abound in robust control [15,21,23,28,32,33,46,47], signal processing [4,5,6,9,25,31] and maximal power transfer [50] in circuit theory, to mention a few. Since the interpolant has a specific interpretation as a transfer function in all these applications, it is important to restrict its degree, and at the same time satisfy all design specifications.…”

Section: Introductionmentioning

confidence: 99%

“…This is done in the context of duality theory of mathematical programming, providing convex optimization problems for determining any interpolant belonging to such a class. In this context, new paradigms for spectral estimation [6,4,5] and robust controller synthesis [7,38,39,40,41,42] have been developed in the scalar-input/scalar-output case.…”

Section: Introductionmentioning

confidence: 99%

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Matrix-valued nevanlinna-pick interpolation with complexity constraint: an optimization approach

Blomqvist

Lindquist

Nagamune

2003

IEEE Trans. Automat. Contr.

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Abstract. Over the last several years a new theory of Nevanlinna-Pick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrix-valued case, also allowing for multiple interpolation points. We parameterize a class of interpolants consisting of "most interpolants" of no higher degree than the central solution in terms of spectral zeros. This is a complete parameterization, and for each choice of interpolant we provide a convex optimization problem for determining it. This is derived in the context of duality theory of mathematical programming. To solve the convex optimization problem, we employ a homotopy continuation technique previously developed for the scalar case. These results can be applied to many classes of engineering problems, and, to illustrate this, we provide some examples. In particular, we apply our method to a benchmark problem in multivariate robust control. By constructing a controller satisfying all design specifications but having only half the McMillan degree of conventional H ∞ controllers, we demonstrate the efficiency of our method.

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A Homotopy Continuation Solution of the Covariance Extension Equation

Byrnes

Fanizza

Lindquist

New Directions and Applications in Control Theory

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Cepstral coefficients, covariance lags, and pole-zero models for finite data strings

Cited by 59 publications

References 26 publications

Time-frequency-moving-average processes: principles and cepstral methods for parameter estimation

Time-frequency-moving-average processes: principles and cepstral methods for parameter estimation

Matrix-valued nevanlinna-pick interpolation with complexity constraint: an optimization approach

A Homotopy Continuation Solution of the Covariance Extension Equation

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