小波变换在金融数据分析中的应用

市场上的数据,从本质上讲都是一种时间序列。它和小波分析中的信号具有相同的特性。因此,完全可以将这些经济时间序列看成信号,应用小波变换进行分析和预测。     

NEW WAVELET BASES FOR NON－HOMOGENEOUS SYMBOLIC SPACE OpS1,1^m AND RELATED KERNEL－DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.     

Improved holographic particle sizing by using absolute values of the wavelet transform

A new method for sizing particle from in-line particle holograms by using absolute values of the wavelet transform is proposed in order to improve accuracy in measurements. The proposed method provides direct calculation of the particle size by using spatial frequency information of a chirp signal at minima position of an envelope function. Simulation and experimental results are presented.     

Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform

A new approach based on the moiré theory and wavelet transform (WT) is proposed for measuring the micro-range distance between a charge-couple-device (CCD) camera and a two-dimensional reference grating. The micro-range distance is determined by measuring the pitch of the moiré pattern image, which is digitized by a CCD camera. A one-dimensional WT algorithm is applied to estimate the pitch of the moiré pattern. Experimental results prove that this technique is very efficient and highly accurate. The moiré range finder is an economic technique for measuring a micro-range distance.     

A new algorithm for fixed design regression and denoising

In this paper, we present a new algorithm to estimate a regression function in a fixed design regression model, by piecewise (standard and trigonometric) polynomials computed with an automatic choice of the knots of the subdivision and of the degrees of the polynomials on each sub-interval. First we give the theoretical background underlying the method: the theoretical performances of our penalized least-squares estimator are based on non-asymptotic evaluations of a mean-square type risk. Then we explain how the algorithm is built and possibly accelerated (to face the case when the number of observations is great), how the penalty term is chosen and why it contains some constants requiring an empirical calibration. Lastly, a comparison with some well-known or recent wavelet methods is made: this brings out that our algorithm behaves in a very competitive way in term of denoising and of compression.     

Wavelet and harmonic filtering for distortion-invariant volume holographic correlation

The wavelet and harmonic filtering method suggested by Zalevsky and Ouzieli is introduced in this paper and adopted in our volume holographic image recognition system. This composite filter combines several scaled versions of the cascaded wavelet and harmonic filter, obtaining high discrimination ability and wide dynamic range of rotation and scale deformations. Optical experiments are conducted to demonstrate the validity and practicability of the algorithm. To the best of our knowledge, this is the first report of using this algorithm in a volume holographic system. Moreover, the separate correlation approach proposed in this paper greatly simplifies the manufacturing process and reduces the cost of the system.     

A pair of orthogonal frames

We start with a characterization of a pair of frames to be orthogonal in a shift-invariant space and then give a simple construction of a pair of orthogonal shift-invariant frames. This is applied to obtain a construction of a pair of Gabor orthogonal frames as an example. This is also developed further to obtain constructions of a pair of orthogonal wavelet frames.     

SOME TOPICS ON WAVELET ANALYSIS

A review of the advance in the theory of wavelet analysis in recent years is given.     

Multivariate calibration of near infrared spectra by orthogonal WAVElet correction using a genetic algorithm

Orthogonal WAVElet correction (OWAVEC) is a pre-processing method aimed at simultaneously accomplishing two essential needs in multivariate calibration, signal correction and data compression, by combining the application of an orthogonal signal correction algorithm to remove information unrelated to a certain response with the great potential that wavelet analysis has shown for signal processing. In the previous version of the OWAVEC method, once the wavelet coefficients matrix had been computed from NIR spectra and deflated from irrelevant information in the orthogonalization step, effective data compression was achieved by selecting those largest correlation/variance wavelet coefficients serving as the basis for the development of a reliable regression model. This paper presents an evolution of the OWAVEC method, maintaining the first two stages in its application procedure (wavelet signal decomposition and direct orthogonalization) intact but incorporating genetic algorithms as a wavelet coefficients selection method to perform data compression and to improve the quality of the regression models developed later. Several specific applications dealing with diverse NIR regression problems are analyzed to evaluate the actual performance of the new OWAVEC method. Results provided by OWAVEC are also compared with those obtained with original data and with other orthogonal signal correction methods.     

小波包去噪信号的分形特征

将分形理论与小波包滤波相结合，用盒维数的大小来评判信号曲线的滤波情况。随着小波包分解尺度的增大，滤波后信号曲线的盒维数逐渐减小，并最后趋于稳定值。因此可以根据盒维数-分解尺度曲线来选择最佳分解尺度。对仿真含噪信号进行了滤波实验，结果表明：即使在信噪比低至0．5时仍能得到较好的结果，并且该法用于毛细管电泳实验数据的处理结果同样令人满意。