Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns

Sampling and Super-resolution of Sparse Signals Beyond the Fourier Domain

Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the natural choice. For example, in holography, low-pass projections of sparse signals are obtained in the Fresnel domain. Similarly, time-varying system identification relies on low-pass projections on the space of linear frequency modulated signals. In this paper, we study the recovery of sparse signals from low-pass projections in the Special Affine Fourier Transform domain (SAFT). The SAFT parametrically generalizes a number of well known unitary transformations that are used in signal processing and optics. In analogy to the Shannon's sampling framework, we specify sampling theorems for recovery of sparse signals considering three specific cases: (1) sampling with arbitrary, bandlimited kernels, (2) sampling with smooth, time-limited kernels and, (3) recovery from Gabor transform measurements linked with the SAFT domain. Our work offers a unifying perspective on the sparse sampling problem which is compatible with the Fourier, Fresnel and Fractional Fourier domain based results. In deriving our results, we introduce the SAFT series (analogous to the Fourier series) and the short time SAFT, and study convolution theorems that establish a convolution--multiplication property in the SAFT domain.Comment: 42 pages, 3 figures, manuscript under revie

Abnormal Gait Behavior Detection for Elderly Based on Enhanced Wigner-Ville Analysis and Cloud Incremental SVM Learning

A cloud based health care system is proposed in this paper for the elderly by providing abnormal gait behavior detection, classification, online diagnosis, and remote aid service. Intelligent mobile terminals with triaxial acceleration sensor embedded are used to capture the movement and ambulation information of elderly. The collected signals are first enhanced by a Kalman filter. And the magnitude of signal vector features is then extracted and decomposed into a linear combination of enhanced Gabor atoms. The Wigner-Ville analysis method is introduced and the problem is studied by joint time-frequency analysis. In order to solve the large-scale abnormal behavior data lacking problem in training process, a cloud based incremental SVM (CI-SVM) learning method is proposed. The original abnormal behavior data are first used to get the initial SVM classifier. And the larger abnormal behavior data of elderly collected by mobile devices are then gathered in cloud platform to conduct incremental training and get the new SVM classifier. By the CI-SVM learning method, the knowledge of SVM classifier could be accumulated due to the dynamic incremental learning. Experimental results demonstrate that the proposed method is feasible and can be applied to aged care, emergency aid, and related fields

Gabor frames and the fractional Fourier transform

Ziel der vorliegenden Diplomarbeit ist, die Auswirkung der fraktionalen Fourier Transformantion auf Gabor Frames mit Gaußscher Fensterfunktion zu untersuchen. Ausgehend von solch einem Gabor-System wird auf jedes Element eine Wurzel der Fourier Transformation angewandt. Die entstehenden Systeme kann man sich geometrisch als eine Familie rotierter Ellipsen vorstellen, die entlang eines Gitters in der Zeit-Frequenz Ebene positioniert sind. Es wird ersichtlich, wie sich die Anordnung dieser Ellipsen in den Frame-Schranken widerspiegelt. Nachdem in den Kapiteln 1 bis 3 die Grundlagen der Fourier- und Gabor Analyisis beschrieben werden, widmet sich Kapitel 4 der fraktionalen Fourier Transformation und ihrer Implementation. Hierzu wird ein etablierter Algorithmus (siehe [3]) mit einem in der NuHAG entwickelten Verfahren verglichen, für das auch eine Konvergenzanalyse durchgeführt wird. Kapitel 5 beschreibt die Ergebnisse numerischer Experimente zu den oben genannten Systemen. Es zeigt sich, dass falls das resultierende System ein Gabor Frame ist, das Verhalten der Frameschranken leicht verständlich, aber durchaus erstaunlich ist. Auÿerdem werden einige Spezialfälle betrachtet, sowie jene Systeme, die durch eine zufällige Wahl der Rotationsparameter entstehen. In Kapitel 6 schließlich finden sich Stabilitätsresultate für die Frame-Schranken der untersuchten Systeme. Diese werden mit Hilfe der Theorie der Wiener- Amalgam Räumen bewiesen