arXiv subjects

Pablo Tarazaga

Publications and source records attributed to Pablo Tarazaga.

2 recordsLinked to original sources

arXiv2025

Effective quality factor of mechanical resonators under complex-frequency excitations

We investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting response is quasi-steady, i.e. after an appropriate transform, the response of the new variable corresponds to the steady state behavior under a harmonic excitation. A procedure is presented to determine the amplitude-frequency response and effective quality factor based on this steady-state behavior. Optimal excitations are identified for both single and multi-degree of freedom systems that result in the amplitude-frequency response approaching that of an undamped system. The feasibility of the proposed method is verified through numerical simulations. Experiments with cantilever beams made of acrylic show a 54-fold increase in the effective quality factor. Our method does not involve any structural modifications and opens avenues for improving detection sensitivity in nondestructive testing and enhancing resolution in micro- and nano-electromechanical sensors.

physics.class-ph↗

arXiv2020

Balanced frames: a useful tool in signal processing with good properties

So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces. Here we discover various advantages of balanced unit norm tight frames in signal processing. They give an exact reconstruction in the presence of systematic errors in the transmitted coefficients, and are optimal when these coefficients are corrupted with noises that can have non-zero mean. Moreover, using balanced frames we can know that the transmitted coefficients were perturbed, and we also have an indication of the source of the error. We analyze several properties of these types of frames. We define an equivalence relation in the set of the dual frames of a balanced frame, and use it to show that we can obtain all the duals from the balanced ones. We study the problem of finding the nearest balanced frame to a given frame, characterizing completely its existence and giving its expression. We introduce and study a concept of complement for balanced frames. Finally, we present many examples and methods for constructing balanced unit norm tight frames.

math.FA↗