Hilda A. Larrondo

A simple adjustable window algorithm to improve FFT measurements

The Fourier spectrum of a periodic signal may be obtained by fast Fourier transform algorithms, but, as is well known, special care must be taken to avoid severe distortions introduced by the sampling process. The main problem is the leakage generated by the truncation required to obtain a finite length sampled data. The usual procedure to reduce leakage is to multiply the sampled signal by a weighting window. Several kinds of windows have been proposed in the literature, and today they are also included in many commercial instruments. A simple alternative procedure is proposed in this paper. It is implemented with a PC compatible data acquisition board (DAQ) and consists of an algorithm that uses decimation and interpolation techniques. This algorithm is equivalent to the use of an adjustable sampling frequency and correspondingly an adjustable window size. Results obtained by this method on both harmonic and polyharmonic signals are empirically analyzed and compared with those given by an instrument with built-in FFT capabilities.

Causality and the entropy–complexity plane: Robustness and missing ordinal patterns

We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, (i) the “causal” entropy–complexity plane [O.A. Rosso, H.A. Larrondo, M.T. Martin, A. Plastino, M.A. Fuentes, Distinguishing noise from chaos, Phys. Rev. Lett. 99 (2007) 154102] and (ii) the estimation of the decay rate of missing ordinal patterns [J.M. Amigo, S. Zambrano, M.A.F. Sanjuan, True and false forbidden patterns in deterministic and random dynamics, Europhys. Lett. 79 (2007) 50001; L.C. Carpi, P.M. Saco, O.A. Rosso, Missing ordinal patterns in correlated noises. Physica A 389 (2010) 2020–2029]. In this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation. The chaotic series studied here was via the logistic map (r=4) to which we added correlated noise (colored noise with f−k Power Spectrum, 0≤k≤2) of varying amplitudes. In such a fashion important insights pertaining to the deterministic component of the original time series can be gained. We find that in the entropy–complexity plane this goal can be achieved without additional computations.

Quantifiers for randomness of chaotic pseudo-random number generators

We deal with randomness quantifiers and concentrate on their ability to discern the hallmark of chaos in time series used in connection with pseudo-random number generators (PRNGs). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely (i) its invariant measure and (ii) the mixing constant. This is of help in answering two questions that arise in applications: (i) which is the best PRNG among the available ones? and (ii) if a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure? Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.

Vibrations of a simply supported plate carrying an elastically mounted concentrated mass

Abstract A large number of papers and technical reports are available on the technically important problem of structural elements executing transverse vibrations and carrying concentrated masses. In general it is assumed that the attachment is perfectly rigid. On the other hand, a rather limited amount of published work is available when the mass is elastically connected to the structure. The system then exhibits a more complex behavior than in the case of rigid attachment. The present study deals with the solution of the title problem using the well-known normal mode, sinusoidal eigenfunction expansions.

Vibrating circular plates with stepped thickness over a concentric circular region: a general, approximate solution

Natural frequencies corresponding to axi‐ and antisymmetric modes of vibration of the structural elements described in the title are studied using the optimized Rayleigh–Ritz approach. It is assumed that the plates are elastically restrained against translation and rotation. The plate amplitude is approximated in terms of polynomial coordinate functions that satisfy the boundary conditions, each one containing an undetermined exponential parameter that allows for the minimization of the eigenvalues under investigation.

Natural frequencies of a Bernoulli beam carrying an elastically mounted concentrated mass

Abstract Civil, naval and ocean engineers are frequently confronted with the problem of mounting dynamic, operational units on structural elements. The designer must be able to determine natural frequencies of the coupled system: structure-motor or engine and its elastic mounting. Frequency coefficients are obtained in the present study for three combinations of boundary conditions: simply supported; simply supported and clamped at both ends.

Transverse vibrations and buckling of circular plates of discontinuously varying thickness subject to an in-plane state of hydrostatic stress

Natural frequencies and buckling loads of circular plates with stepped thickness over a concentric circular region are determined using the optimized Rayleigh-Ritz method. The solution is obtained for the case of edges elastically restrained against rotation and translation.

Zipping Characterization of Chaotic Sequences Used in Spread Spectrum Communication Systems

In this paper finite sequences, known as Pseudo Noise codes (PN‐codes) are studied. PN‐codes are used in Spread Spectrum Digital Systems (SSDS), a widely employed wireless communication technique. The selection of the best “set of PN‐codes” (PN‐family) is an important issue in SSDS. This selection is based on a very involved statistical analysis. This paper presents three contributions in this field: the first contribution is the definition of new global quantifiers instead of those used in the engineering literature. The second contribution is to show that a quantifier based on the Zipping Complexity Measure may be a global optimization quantifier of the whole system. Finally a comparison between usual PN‐families and chaotic generated PN‐families is presented, showing that chaotic systems are competitive in this application field.

FPGA implementation of a chaotic oscillator using RK4 method

The dual deterministic-stochastic behavior of chaotic systems (CS) makes them extremely interesting in electronic engineering as CS may replace noise sources in different applications. Consequently it is convenient to have hardware implementations for both, analog and digital versions. Discrete components, Micro Controllers, Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGAs) are possible choices.

A low-cost fiber-optic system for monitoring the state of structural health of a mechanical cable

Abstract Methods for evaluating the structural health of mechanical cables and detecting their imminent failure could prevent the loss of valuable equipment and, more importantly, the possible loss of human life. The non-destructive test methods available are: thorough visual examination and measurement of the external diameter; X-rays; (induced) wave propagation; acoustic emission; magnetostrictive sensors; infrared detection. A new method which employs a commercial optical fiber for detecting the breakage of individual wires in a rope is proposed in the present paper.