Bogdan Dumitrescu

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In this paper, we consider infinite impulse response (IIR) filter design where both magnitude and phase are optimized using a weighted and sampled least-squares criterion. We propose a new convex stability domain defined by positive realness for ensuring the stability of the filter and adapt the Steiglitz-McBride (SM), Gauss-Newton (GN), and classical(More)
We propose a characterization of multivariate trigonometric polynomials that are positive on a given frequency domain. The positive polynomials are parameterized as a linear function of sum-of-squares polynomials and so semidefinite programming (SDP) is applicable. The frequency domain is expressed via the positivity of some trigonometric polynomials. We(More)
We show that an H<sub>infin</sub> optimization problem related to fractional delay approximation can be formulated as a semideflnite programming (SDP) problem and thus solved reliably. Particularly, given the finite-impulse-response (FIR) filter H(z), we find the FIR filter G(z) of given degree such that ||G(z) - z<sup>-1/2</sup>H(z)||<sub>infin</sub> is(More)
We discuss descriptions of convex domains containing Schur polynomials, built around a given Schur polynomial. We show that the domain described by a positive realness constraint always contains the domain characterized by Rouche&#x0301;'s theorem. We also show how to handle computationally the positive realness condition, using semidefinite programming, in(More)
The problem of training a dictionary for sparse representations from a given dataset is receiving a lot of attention mainly due to its applications in the fields of coding, classification and pattern recognition. One of the open questions is how to choose the number of atoms in the dictionary: if the dictionary is too small then the representation errors(More)
  • B. Dumitrescu
  • Proceedings of the 6th Nordic Signal Processing…
  • 2004
We present an algorithm for the least squares optimization of 2-D IIR filters with separable or nonseparable denominator. The algorithm is iterative and each iteration consists of solving a semidefinite programming problem. We adapt the Gauss-Newton idea which outcomes to a convex approximation of the optimization criterion. The stability of the 2-D IIR(More)
Simplified procedures for quasi-equiripple infinite-impulse response (IIR) filter design are proposed. The procedures can be applied in designs where the number of poles is low compared to the number of zeros. The design is initialized with an IIR filter optimizing a least squares criterion. In the simplified procedures, namely simplified iterative(More)
In this letter we give efficient solutions to the construction of structured dictionaries for sparse representations. We study circulant and Toeplitz structures and give fast algorithms based on least squares solutions. We take advantage of explicit circulant structures and we apply the resulting algorithms to shift-invariant learning scenarios. Synthetic(More)