This study examines the price level and volatility interaction between international staple food and cash crop futures price indices. Understanding the relationship between these commodities bears significant implications for low-income food deficit countries that depend on cash crops to finance food import bills. We use a wavelet analysis to decompose the price indices and then apply a BEKK-MGARCH (Baba, Engle, Kraft and Kroner–multivariate generalized autoregressive conditional heteroskedasticity) approach to analyze the relationship across timescales. Results indicate the level of correlation and volatility linkages are strongest at lower frequencies (longer run) than at higher timescales (short run), with information running from staple food to cash crop markets.

Temporal oscillations of F2 layer critical frequency are direct outcome of solar EUV variability. The hourly data of F2 layer critical frequency (foF2) during solar cycle 23 over eight ionosonde stations which falls within same longitudinal span are evaluated using Continuous Wavelet Transform (CWT) to estimate the ionospheric variations. The quasi triennial, annual, semiannual, 27 day and diurnal variations of foF2 are clearly evident in the wavelet power spectra of all the stations. Quasi triennial oscillations which show a clear latitudinal dependence is more evident in southern stations. A strong quasi biennial oscillation (QBO) is also noticed in higher latitudes which was not observable in equatorial latitude. The present study reveals that the semiannual variations are more obvious over the annual variation in the equatorial and low latitude stations while the annual variations are prominent in higher latitudes.

The objective of this study was to develop an automated monitoring system to detect lameness in group-housed sows early and reliably on the basis of acceleration data sampled from ear tags. To this end, acceleration data from ear tags were acquired from an experimental system deployed at the Futterkamp Agriculture Research Farm from May 2012 until November 2013. The developed method performs a wavelet transform for each individual sow’s time series of total acceleration. Feature series are then computed by locally estimating the energy, variation and variance in a small moving window. These feature series are then further decomposed into uniform level sets. From these series of level sets, the highest and lowest levels are monitored for lameness detection. To that end, they are split into a past record to serve as reference data representing a sow’s expected behaviour. The deviations between the reference and the remaining detection part of current data, termed feature activated, were then utilised to possibly indicate a lameness condition. The method was applied to a sample of 14 sows, seven of which were diagnosed as lame by a veterinarian on the last day of the sampling period of 14 days each. A prediction part of 3 days was set. Feature activated were clearly separable for the lame and healthy group with means of 8.8 and 0.8, respectively. The day-wise means were 1.93, 9.47 and 15.16 for the lame group and 0.02, 1.13 and 1.44 for the healthy group. A threshold could be set to completely avoid false positives while successfully classifying six lame sows on at least one of the 2 last days. The accuracy values for this threshold were 0.57, 0.71 and 0.78 when restricting to data from the particular day. A threshold that maximised the accuracy achieved values of 0.57, 0.79 and 0.93. Thus, the method presented seems powerful enough to suggest that an individual classification from ear tag-sampled acceleration data into lame and healthy is feasible without previous knowledge of the health status, but has to be validated by using a larger data set.

Total variation (TV) and wavelet L1 norms have often been used as regularization terms in image restoration and reconstruction problems. However, TV regularization can introduce staircase effects and wavelet regularization some ringing artifacts, but hybrid TV and wavelet regularization can reduce or remove these drawbacks in the reconstructed images. We need to compute the proximal operator of hybrid regularizations, which is generally a sub-problem in the optimization procedure. Both TV and wavelet L1 regularisers are nonlinear and non-smooth, causing numerical difficulty. We propose a dual iterative approach to solve the minimization problem for hybrid regularizations and also prove the convergence of our proposed method, which we then apply to the problem of MR image reconstruction from highly random under-sampled k-space data. Numerical results show the efficiency and effectiveness of this proposed method.

In this work we introduce a class of discrete groups containing subgroups of abstract translations and dilations, respectively. A variety of wavelet systems can appear as $\pi \left( \Gamma \right)\psi $, where $\pi $ is a unitary representation of a wavelet group and $\Gamma $ is the abstract pseudo-lattice $\Gamma $. We prove a sufficent condition in order that a Parseval frame $\pi \left( \Gamma \right)\psi $ can be dilated to an orthonormal basis of the form $\tau \left( \Gamma \right)\Psi $, where $\tau $ is a super-representation of $\pi $. For a subclass of groups that includes the case where the translation subgroup is Heisenberg, we show that this condition always holds, and we cite familiar examples as applications.

In this paper an optimal path planning method based on a new evolutionary algorithm is presented for higher order robotic systems. It is a combination of immune system and wavelet mutation. By increasing the system's dimensions, the complexity of algorithm grows linearly. The obtained results have been compared with other optimal path producing algorithms, and its excellence in terms of optimality has been proved. Strengths of this method are simplicity in large-scale path planning, being free of most of the common deadlocks in usual method, and ability to obtain more optimized results than other similar methods. The effectiveness of this approach on simulation case studies for a three-link planar robot and 5 degrees of freedom mobile manipulators as well as an experiment for a mobile robot called K-joniour is shown.

Content-aware image resizing (CAIR) is desired because it preserves prominent regions in a resized image. However, CAIR requires high computational complexity to perform in mobile devices, though it is desired for these displays. Moreover, transmitting the side information for CAIR from the encoder is a problem since it usually requires high bitrates compared with those for image data. In this paper, we present a rate-dependent CAIR method that produce various retargeting results based on the bitrates for side information. Furthermore, we apply the proposed technique to wavelet-based image coding. Our proposed content-aware image coding method provides good performances for both CAIR and image coding.

A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an orthonormal basis in ${{L}^{2}}({{\mathbb{R}}^{d}})$. While tensor products of uniscaled MRAs provide simple examples we construct many nonseparable higher rank wavelets. In particular we construct Latin square wavelets as rank 2 variants of Haar wavelets. Also we construct nonseparable scaling functions for rank 2 variants of Meyer wavelet scaling functions, and we construct the associated nonseparable wavelets with compactly supported Fourier transforms. On the other hand we show that compactly supported scaling functions for biscaled MRAs are necessarily separable.

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and nonperiodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown.

Dans la maintenance conditionnelle de composants mécaniques par analyse vibratoire, on distingue deux types d'analyses qui sont nécessaires pour l'obtention d'un diagnostic fiable. La première analyse réside dans la détection de défauts potentiels et il existe actuellement différentes méthodes abouties basées sur le traitement des signaux vibratoires permettant la localisation d'un défaut. On peut citer parmi ces méthodes l'analyse spectrale (à résolution constante (RC) ou à pourcentage de bandes constant (PBC)), l'analyse d'enveloppe, l'analyse cepstrale, l'analyse temps-fréquences ou l'analyse temps-échelles (ondelettes). La seconde analyse s'intéresse quant à elle à la détermination et l'évaluation de la sévérité d'un défaut détecté pour estimer l'influence de ce défaut sur le fonctionnement d'un mécanisme. Les indicateurs vibratoires, qui permettent de pouvoir corréler la sévérité d'un défaut à sa signature vibratoire, sont des indicateurs dits globaux qui sont basés sur l'analyse statistique d'un signal temporel. Cependant, les signaux issus de capteurs accélérométriques sont le résultat d'un mélange de sources de vibrations, sources pouvant être attribuées à un ou plusieurs défauts et sont généralement pollués par du bruit. Ce travail présente les trois principales méthodes de débruitage et l'étude de leur influence sur les paramètres scalaires (kurtosis, facteur crête) et ce dans le cadre de la détection de défauts de type écaillage de roulements.

Experiments were made with 14 MEMS sensors situated along the span of a circular cylinder whose aspect ratio was 5. The signals of the MEMS sensors were sampled simultaneously as flow over the cylinder at Reynolds numbers of 104. The results of Wavelet analysis of the signals indicate that the percentage of time during which strong three-dimensionality of vortex shedding was detected is about 10%.As noted, strong three-dimensionality took place when the fluctuating amplitude of the signals was severely modulated and the vortex shedding frequency reduced appeared abnormally high or low. Further noted was that the addition of a splitter plate of 0.5 or one diameter in length behind the circular cylinder was not able to suppress the three-dimensionality of the flow.

The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.

A typical problem of elastic wave methods, such as the impact echo method, is due to peak detection based solely on amplitude spectrum. Current study aims to improve the feature identification of impact-echo signals obtained from buried objects in concrete slabs. Steel rebar, steel tubes, and PVC tubes embedded in a concrete slab are tested. Numerical simulations are carried out based on models constructed using the finite element method. The received signals, both experimental and simulated, are analyzed using both fast Fourier transform and continuous wavelet transform (CWT). The amplitude spectra can only provide global information and lose some important local effects of frequency components. This can be resolved by continuous wavelet transform for preserving the transient effects in the frequency domain. Localized spectral contents are analyzed and thus better understanding is achieved for the impulse responses due to different objects below the surface of the concrete slab. Features related to steel rebar, PVC and steel tubes are readily identified in the coefficient plot of wavelet coefficients. Multiple reflections and vibration modes related to various characteristics of wave propagation in the concrete slab can now be decomposed into distinctive frequency bands with different time durations. The result of CWT provides more information and is easier to interpret than that of the spectral analysis. The same peak frequency found in the amplitude spectrum is now distinguishable between PVC and steel tubes at a resolution of 0.1kHz or better. Such findings provide a more effective way to pick up true rebar signals using the impact-echo method.

We make use of the Beylkin-Coifman-Rokhlin wavelet decomposition algorithm on the Calderón-Zygmund kernel to obtain some fine estimates on the operator and prove the T(l) theorem on Besov and Triebel-Lizorkin spaces. This extends previous results of Frazier et al., and Han and Hofmann.

Attitude estimation systems often use two or more different sensors to increase reliability and accuracy. Although gyroscopes do not have problems like limited range, interference, and line of sight obscuration, they suffer from slow drift. On the other hand, inclinometers are drift-free but they are sensitive to transverse accelerations and have slow dynamics. This paper presents an extended Kalman filter (EKF)-based data fusion algorithm which utilizes the complementary noise profiles of these two types of sensors to extend their limits. To avoid complexities of dynamic modelling of the platform and its interaction with the environment, gyro modelling will be used to implement indirect (error state) form of the Kalman filter. The great advantage of this approach is its independence from the structure of the platform and its applicability to any system with a similar set of sensors. Separate bias formulation of the Kalman filter will be used to reduce the computational complexity of the algorithm. In addition, a systematic approach based on wavelet decomposition will be utilized to estimate noise covariances used in the Kalman filter formulation. This approach solves many of the convergence problems encountered in the implementation of EKF due to the choice of covariance matrices. Experimental implementation of the estimator shows the excellent performance of the filter.

Arbitrage-free prices u of European contracts on risky assets whoselog-returns are modelled by Lévy processes satisfya parabolic partial integro-differential equation (PIDE) $\partial_t u + {\mathcal{A}}[u] = 0$ .This PIDE is localized tobounded domains and the error due to this localization isestimated. The localized PIDE is discretized by theθ-scheme in time and a wavelet Galerkin method with N degrees of freedom in log-price space. The dense matrix for ${\mathcal{A}}$ can be replaced by a sparse matrix in the wavelet basis, and the linear systemsin each implicit time step are solved approximativelywith GMRES in linear complexity. The total work of the algorithm for M time steps is bounded byO(MN(log(N))2) operations and O(Nlog(N)) memory.The deterministic algorithm gives optimal convergence rates (up to logarithmic terms) for the computed solutionin the same complexity as finite difference approximationsof the standard Black–Scholes equation.Computational examples for various Lévy price processes are presented.

We consider a unitary representation of a discrete countable abelian group on a separable Hilbert space which is associated to a cyclic generalized frame multiresolution analysis. We extend Robertson’s theorem to apply to frames generated by the action of the group. Within this setup we use Stone’s theorem and the theory of projection valued measures to analyze wandering frame collections. This yields a functional analytic method of constructing a wavelet from a generalized frame multiresolution analysis in terms of the frame scaling vectors. We then explicitly apply our results to the action of the integers given by translations on ${{L}^{2}}(\mathbb{R})$.

The aim of this study was to assess the error made by violating the assumption of stationarity when using Fourier analysis for spectral decomposition of heart period power. A comparison was made between using Fourier and Wavelet analysis (the latter being a relatively new method without the assumption of stationarity). Both methods were compared separately for stationary and nonstationary segments. An ambulatory device was used to measure the heart period data of 40 young and healthy participants during a psychological stress task and during periods of rest. Surprisingly small differences (<1%) were found between the results of both methods, with differences being slightly larger for the nonstationary segments. It is concluded that both methods perform almost identically for computation of heart period power values. Thus, the Wavelet method is only superior for analyzing heart period data when additional analyses in the time-frequency domain are required.

It is well known that the compactly supported wavelets cannot belong to the class ${{C}^{\infty }}\,(\text{R})\,\cap \,{{L}^{2}}\,(R)$. This is also true for wavelets with exponential decay. We show that one can construct wavelets in the class ${{C}^{\infty }}\,(\text{R})\,\cap \,{{L}^{2}}\,(R)$ that are “almost” of exponential decay and, moreover, they are band-limited. We do this by showing that we can adapt the construction of the Lemarié-Meyer wavelets $[\text{LM }\!\!]\!\!\text{ }$ that is found in $[\text{BSW}]$ so that we obtain band-limited, ${{C}^{\infty }}$-wavelets on $R$ that have subexponential decay, that is, for every $0<\varepsilon <1$, there exits ${{C}_{\in }}\,>\,0$ such that $|\psi (x)|\le {{C}_{\varepsilon }}{{e}^{-|x{{|}^{1-\varepsilon }}}}$, $x\in \text{R}$. Moreover, all of its derivatives have also subexponential decay. The proof is constructive and uses the Gevrey classes of functions.