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- Tryphon T. Georgiou, Johan Karlsson, Mir Shahrouz Takyar
- IEEE Transactions on Signal Processing
- 2009

We present an axiomatic framework for seeking distances between power spectral density functions. The axioms require that the sought metric respects the effects of additive and multiplicative noise in reducing our ability to discriminate spectra, as well as they require continuity of statistical quantities with respect to perturbations measured in the… (More)

It is a well-known fact that set-point following, in linear control systems, requires an integrator in the feedback loop. However, such an integrator introduces phase lag which may often have a destabilizing effect. A variety of options exist for adding lead to mediate this effect. In this paper we consider yet another option, a fractional integrator. We… (More)

- Mir Shahrouz Takyar, Ali Nasiri Amini, Tryphon T. Georgiou
- IEEE Trans. Automat. Contr.
- 2008

We present an approach for feedback design which is based on recent developments in analytic interpolation with a degree constraint. Performance is cast as an interpolation problem with bounded analytic functions. Minimizers of a certain weighted-entropy functional provide interpolants having degree less than the number of constraints. The choice of weight… (More)

- Mir Shahrouz Takyar, Tryphon T. Georgiou
- IEEE Trans. Automat. Contr.
- 2010

- Ali Nasiri Amini, Mir Shahrouz Takyar, Tryphon T. Georgiou
- 2006 IEEE International Conference on Acoustics…
- 2006

We present a technique for spectral analysis in the context of multi-rate sampling by a collection of sensors. Correlation of the time-domain samples gives rise to moment constraints for the power spectrum. A homotopy-based technique is then used to identify consistent power spectra. The spectra we obtain are at a minimum distance in the Kullback-Leibler… (More)

The parametrization of solutions to scalar interpolation problems with a degree constraint relies on the concept of spectral-zeros –these are the poles of the inverse of a corresponding spectral factor. In fact, under a certain degree constraint, the spectral-zeros are free (modulo a stability requirement) and parameterize all solutions. The subject of this… (More)

We present a family of metrics for power spectra based on the Monge-Kantorivic transportation distances. These metrics are constructed so that distances reduce with additive and multiplicative noise, reflecting the intuition that noise typically reduces our ability to discriminate spectra. In addition, perturbations measured in these metrics are continuous… (More)

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