The sample autocorrelation function and the detection of long-memory processes

The detection of long-range dependence in time series analysis is an important task to which this paper contributes by showing that whilst the theoretical definition of a long-memory (or long-range dependent) process is based on the autocorrelation function, it is not possible for long memory to be identified using the sum of the sample autocorrelations, as usually defined. The reason for this is that the sample sum is a predetermined constant for any stationary time series; a result that is independent of the sample size. Diagnostic or estimation procedures, such as those in the frequency domain, that embed this sum are equally open to this criticism. We develop this result in the context of long memory, extending it to the implications for the spectral density function and the variance of partial sums of a stationary stochastic process. The results are further extended to higher order sample autocorrelations and the bispectral density. The corresponding result is that the sum of the third order sample (auto) bicorrelations at lags h,k≥1, is also a predetermined constant, different from that in the second order case, for any stationary time series of arbitrary length.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Pitch detection algorithms based on zero-cross rate and autocorrelation function for musical notes

This paper discusses two pitch detection algorithms (PDA) for simple audio signals which are based on zero-cross rate (ZCR) and autocorrelation function (ACF). As it is well known, pitch detection methods based on ZCR and ACF are widely used in signal processing. This work shows some features and problems in using these methods, as well as some improvements developed to increase their performance. © 2008 IEEE.

Recognizing Decomposition of a Partial Boolean Function

A hard combinatorial problem is investigated which has useful application in design of discrete devices: the two-block decomposition of a partial Boolean function. The key task is regarded: finding such a weak partition on the set of arguments, at which the considered function can be decomposed. Solving that task is essentially speeded up by the way of preliminary discovering traces of the sought-for partition. Efficient combinatorial operations are used by that, based on parallel execution of operations above adjacent units in the Boolean space.

Improved damage detectability in a wind turbine blade by optimal selection of vibration signal correlation coefficients

Piotr Omenzetter and Simon Hoell’s work within the Lloyd’s Register Foundation Centre for Safety and Reliability Engineering at the University of Aberdeen is supported by Lloyd’s Register Foundation. The Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research.

Improved damage detectability in a wind turbine blade by optimal selection of vibration signal correlation coefficients

Piotr Omenzetter and Simon Hoell’s work within the Lloyd’s Register Foundation Centre for Safety and Reliability Engineering at the University of Aberdeen is supported by Lloyd’s Register Foundation. The Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research.

Perception of concurrent sentences with harmonic or frequency-shifted voiced excitation:performance of human listeners and of computational models based on autocorrelation

Keyword identification in one of two simultaneous sentences is improved when the sentences differ in F0, particularly when they are almost continuously voiced. Sentences of this kind were recorded, monotonised using PSOLA, and re-synthesised to give a range of harmonic ?F0s (0, 1, 3, and 10 semitones). They were additionally re-synthesised by LPC with the LPC residual frequency shifted by 25% of F0, to give excitation with inharmonic but regularly spaced components. Perceptual identification of frequency-shifted sentences showed a similar large improvement with nominal ?F0 as seen for harmonic sentences, although overall performance was about 10% poorer. We compared performance with that of two autocorrelation-based computational models comprising four stages: (i) peripheral frequency selectivity and half-wave rectification; (ii) within-channel periodicity extraction; (iii) identification of the two major peaks in the summary autocorrelation function (SACF); (iv) a template-based approach to speech recognition using dynamic time warping. One model sampled the correlogram at the target-F0 period and performed spectral matching; the other deselected channels dominated by the interferer and performed matching on the short-lag portion of the residual SACF. Both models reproduced the monotonic increase observed in human performance with increasing ?F0 for the harmonic stimuli, but not for the frequency-shifted stimuli. A revised version of the spectral-matching model, which groups patterns of periodicity that lie on a curve in the frequency-delay plane, showed a closer match to the perceptual data for frequency-shifted sentences. The results extend the range of phenomena originally attributed to harmonic processing to grouping by common spectral pattern.

Seasonality of suicide in the city of Sao Paulo, Brazil, 1979-2003

OBJECTIVE: To evaluate suicide seasonality in the city of São Paulo within an urban area and tropical zone. METHOD: Suicides were evaluated using the chi-square test and analysis of variance (ANOVA) by comparing monthly, quarterly and half-yearly variations, differentiating by gender. Analyses of time series were carried out using the autocorrelation function and periodogram, while the significance level for seasonality was confirmed with the Fisher's test. RESULTS: The suicides of the period between 1979 and 2003 numbered 11,434 cases. Differences were observed in suicides occurring in Spring and Autumn for the total sample (ANOVA: p-value = 0.01), and in the male sample (ANOVA: p-value = 0.02). For the analysis of time series, seasonality was significant only for the period of 7 months in the male sample (p-value = 0.04). DISCUSSION: In this study, no significant seasonal differences were observed in the occurrences of suicides, with the exception of the male sample. The differences observed did not correspond with the pattern described in studies carried out in temperate zones. Some of the climatic particularities of the tropical zone might explain the atypical pattern of seasonality of suicides found in large populations within an urban area and tropical zone.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Prescription footwear for severe injuries of foot and ankle: effect on regularity and symmetry of the gait assessed by trunk accelerometry.

After foot and/or ankle fracture, the restoration of optimal gait symmetry is one of the criteria of recovery. Orthotic insoles and orthopaedic shoes improve gait symmetry and regularity by controlling joint motion and improving alignment. The aim of the present study was to assess the effect of prescription footwear on gait quality by using accelerometers attached to the lower back. Sixteen adult patients with persistent disability after ankle and/or foot fractures performed two 30-s walking trials with and without prescription footwear (insoles and stabilizing shoes). Sixteen control subjects were also tested for comparison. The autocorrelation function was computed from the acceleration signal and the first two dominant periods were assessed (d1 and d2). Two parameters were used: (1) Stride Regularity (SR) which expresses the similarity between strides over time (d2), and (2) Stride Symmetry (SS) a ratio (d1/d2) which expresses the left/right similarity of gait independently of repeatability in the successive movements of each limb. In control subjects, SR and SS were 0.86+/-0.05 (correlation coefficient) and 81+/-10%, respectively. In the patient group, the effect of footwear was significant (SR: 0.88+/-0.06 vs. 0.90+/-0.05, SS: 38+/-23% vs. 46+/-27%). Pain was also significantly reduced (-34%). By using a rapid and low-cost method, we objectively quantified gait quality improvement after footwear intervention, concomitant to pain reduction. Substantial inter-patient variability in the footwear outcome was observed. In conclusion, we believe that trunk accelerometry can be a useful tool in the field of gait rehabilitation.

Short-time dynamics of colloidal suspensions in confined geometries

We analyze the short-time dynamical behavior of a colloidal suspension in a confined geometry. We analyze the relevant dynamical response of the solvent, and derive the temporal behavior of the velocity autocorrelation function, which exhibits an asymptotic negative algebraic decay. We are able to compare quantitatively with theoretical expressions, and analyze the effects of confinement on the diffusive behavior of the suspension.

Effect of drift on segregation in two-component diffusion-limited aggregation

An effect of drift is investigated on the segregation pattern in diffusion-limited aggregation (DLA) with two components (A and B species). The sticking probability PAB (=PBA) between the different species is introduced into the DLA model with drift, where the sticking probability PAA (=PBB) between the same species equals 1. By using computer simulation it is found that the drift has an important effect on not only the morphology but also the segregation pattern. Under the drift and the small sticking probability, a characteristic pattern appears where elongated clusters of A species and of B species are periodically dispersed. The period decreases with increasing drift. The periodic structure of the deposits is characterized by an autocorrelation function. The shape of the cluster consisting of only A species (or B species) shows a vertically elongated filamentlike structure. Each cluster becomes vertically longer with decreasing sticking probability PAB. The segregation pattern is distinctly different from that with no drift and a small sticking probability PAA. The effect of the concentration on the segregation pattern is also shown.