小波变换在雷达信号处理中的应用

，小波变换理论是傅里叶分析的重大进展，它已成为当今从应用数学到信号与图像处理等众多领域的研究热点。本文综述了傅里叶变换、加窗傅氏变换、小波变换的特性，讨论了将小波变换应用于雷达领域的前景。     

Multiscale methods for data on graphs and irregular multidimensional situations

Summary.  For regularly spaced one-dimensional data, wavelet shrinkage has proven to be a compelling method for non-parametric function estimation. We create three new multiscale methods that provide wavelet-like transforms both for data arising on graphs and for irregularly spaced spatial data in more than one dimension. The concept of scale still exists within these transforms, but as a continuous quantity rather than dyadic levels. Further, we adapt recent empirical Bayesian shrinkage techniques to enable us to perform multiscale shrinkage for function estimation both on graphs and for irregular spatial data. We demonstrate that our methods perform very well when compared with several other methods for spatial regression for both real and simulated data. Although we concentrate on multiscale shrinkage (regression) we present our new 'wavelet transforms' as generic tools intended to be the basis of methods that might benefit from a multiscale representation of data either on graphs or for irregular spatial data.     

—个抛物型方程逆问题的Fourier和小波正则化方法

考虑非标准的一维逆热传导方程的定解问题。问题是不适定性的，即g（t）微小扰动会引起解的很大误差。通过Fourier方法，舍去g（t）的高频成分来正则化问题并给出了误差估计；利用Meyer小波在频域中的紧支撑性滤除g（t）的高频成分并结合Galerkin方法建立了正则化方法，给出了误差估计；对上述两种方法给出了数值实验并进行了比较和讨论。     

用Delphi实现基于小波变换的JPEG2000压缩

本文从Delphi的一般应用方法入手,给出了实现基于小波变换的JPEG2000压缩方法,详细的阐述小波变换的理论,介绍了实现过程中的技巧。     

Differentiating noisy radiocommunications signals: wavelet estimation of a derivative in the presence of heteroscedastic noise

Summary.  Radio scientists require estimates of the rate of change in rain-induced signals. Unfortunately, these signals are observed in the presence of atmospheric noise, which has a variance that is dependent on temperature, pressure and other climatic variables. We develop a systematic approach to the problem, using wavelet differentiation combined with coefficient-dependent thresholding, and illustrate the considerable benefits that this provides over more conventional techniques.     

Computing functional estimators of spatiotemporal long-range dependence parameters in the spectral-wavelet domain

This paper addresses the problem of parameter estimation of spatiotemporal long-range dependence models from functional spectral data. Four wavelet-based functional estimation algorithms are proposed to approximate the multidimensional strong-dependence parameter, characterizing the covariance tail behavior of the spatiotemporal non-self-similar model class studied in [Frías et al., 2006b] and [Frías et al., 2009]. Wavelet regression is performed in all of them. Functional spectral data are averaged in the first and fourth algorithms, while, in the second and third ones, averaging is performed on the wavelet regression estimates. Smoothing over the wavelet translation parameter is performed, within each resolution level, only in Algorithms 3 and 4. A simulation study is carried out to illustrate the performance of the four functional estimation algorithms proposed under different scenarios.     

The cross-impact between financial markets,Covid-19 pandemic,and economic sanctions: The case of Iran

The main financial markets in the Iranian Economy include the stock exchange, foreign exchange, oil, and gold markets. The sharp fluctuations in these markets, especially those caused by the severe sanctions imposed on Iran in May 2018, and the pandemic outbreak of Covid-19 have led to more confusion and uncertainty among investors. One of the effective approaches to examine such unstable conditions is to study the co-movement(s) between markets to identify the leading variable(s). Thus, in the present study, Wavelet Coherence Analysis was applied to examine the co-movements between markets in a time period from September 2014 to June 2020, as an intense period of uncertainty in Iran. In other words, in this study, the markets were investigated in different sub-periods. Also, the Segmented Regression was performed to estimate the impact of sanctions and the Covid-19 pandemic on the co-movements of financial markets in Iran.The results showed that the oil price had a low co-movement with the other three markets, i.e. stock exchange, exchange rate, and gold markets. Thus, the oil market can be a suitable alternative for risk aversion investors. Meanwhile, the oil market could also act as a source of finance for the government during the sanctions period. That possibly explains the recent decision by the Iranian government to use the oil market to finance its budget deficit. Between the exchange rate and gold price, the gold price was identified as the leading variable. While the exchange rate and gold price did not show a significant co-movement in stable conditions, they did show a significant co-movement in unstable conditions, as in times of sanctions or during a global pandemic and thus influenced the investors’ portfolio risk. This result is important from a policy-making perspective. Based on this result, the policymakers can, especially during crises and unstable conditions, control the gold market and make it more stable by managing the foreign exchange market.     

A Note on the Effect of Wavelet Choice on the Estimation of the Evolutionary Wavelet Spectrum

The locally stationary wavelet process model assumes some underlying wavelet family in order to generate the process. Analyses of such processes also assume that the same wavelet family is used to obtain unbiased estimates of the wavelet spectrum. In practice this would not typically be possible since, a priori, the underlying wavelet family is not known. This article considers the effect of wavelet choice within this setting. A particular focus is given to the estimation of the evolutionary wavelet spectrum due to its importance in many reported applications.     

A Fast Wavelet Algorithm for Analyzing One-Dimensional Signal Processing and Asymptotic Distribution of Wavelet Coefficients With Numerical Example and Simulation

In this article, we consider a sample point (t _j , s _j ) including a value s _j  = f(t _j ) at height s _j and abscissa (time or location) t _j . We apply wavelet decomposition by using shifts and dilations of the basic Häar transform and obtain an algorithm to analyze a signal or function f. We use this algorithm in practical to approximating function by numerical example. Some relationships between wavelets coefficients and asymptotic distribution of wavelet coefficients are investigated. At the end, we illustrate the results on simulated data by using MATLAB and R software.     

Finite Sample Comparison of Parametric,Semiparametric, and Wavelet Estimators of Fractional Integration

ABSTRACT

In this paper we compare through Monte Carlo simulations the finite sample properties of estimators of the fractional differencing parameter, d. This involves frequency domain, time domain, and wavelet based approaches, and we consider both parametric and semiparametric estimation methods. The estimators are briefly introduced and compared, and the criteria adopted for measuring finite sample performance are bias and root mean squared error. Most importantly, the simulations reveal that (1) the frequency domain maximum likelihood procedure is superior to the time domain parametric methods, (2) all the estimators are fairly robust to conditionally heteroscedastic errors, (3) the local polynomial Whittle and bias-reduced log-periodogram regression estimators are shown to be more robust to short-run dynamics than other semiparametric (frequency domain and wavelet) estimators and in some cases even outperform the time domain parametric methods, and (4) without sufficient trimming of scales the wavelet-based estimators are heavily biased.