共查询到19条相似文献,搜索用时 109 毫秒
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《数学的实践与认识》2017,(5)
针对分数阶Fourier变换在信号处理中应用的广泛性,引入了分数阶尺度函数与分数阶小波变换的概念.运用分数阶Fourier变换与时频分析方法研究了分数阶多分辨分析与尺度函数的构造方法,刻画分数阶尺度函数的特征.得到分数阶尺度函数存在的充要条件. 相似文献
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LFM(线性调频)信号是一类重要的非平稳信号,其完全被初始频率和调频斜率两个参量表征,而LFM信号的检测与估计问题是信号处理中最为重要的研究热点之一.由于调频信号在时频平面内有较好的聚集性,通常使用时频分析的方法对其进行检测和估计.线性正则变换是经典时频分布的广义形式,对LFM信号具有很好的能量聚集特性,在现有的线性正则域Hilbert变换的基础上,提出了一种不需要谱峰搜索而快速检测LFM信号和估计其参数的方法,并且通过仿真实例验证了所提出方法的优越性. 相似文献
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正交小波包及其在数字信号压缩中的应用 总被引:5,自引:0,他引:5
正交小波包是正交多分辨分析构造正交小波思想的自然延伸,正交小波包变换可以进一步分割小波空间,解决小波变换“高频低分辨”的问题,为数字信号处理提供获得高频高分辨效果的分析工具。最后,将小波包分析用于数字信号压缩问题的研究,获得了很好的变换压缩效果 相似文献
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一种利用多通道小波变换去噪的算法 总被引:1,自引:0,他引:1
通过对多通道小波和小波变换以及奇异信号的小波变换特性的讨论和分析,提出了一种利用M道小波变换去噪的算法,并利用此算法对加噪信号进行了模拟实验,实验结果表明,该算法简便,易于编程实现且去噪效果理想。 相似文献
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小波变换及其在时-频分析中的应用 总被引:7,自引:0,他引:7
冉启文、王建赜.小波变换及其在时-频分析中的应用.小波变换作为数据处理和数字信号处理的一种新方法,具有良好的时-频局部化能力,为信号的时-频分析提供了有效的分析方法。本文详细讨论了小波分析的时-频特性,同时给出这个性质的几个典型应用 相似文献
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小波分析方法及其应用 总被引:2,自引:0,他引:2
2.正交小波和多分辨分析前面已经指出,连续小波变换和离散小波变换具有统一的形式,特别是正交小波的引入,使一个小波函数的“伸缩”和“平移”产生的函数族构成函数空间L2(R)的一个标准正交基,这给信号分析和一般的数据处理带来许多方便。这样就产生一个问题:... 相似文献
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We introduce here fractional Cohen class of time-frequency distributions (FCCTFDs) containing fractional modulations which is kernel of fractional Fourier transform (FFT). The fractional modulation depends on angular parameter α and can be interpreted as a rotation by an angle α in time-frequency plane. This distribution promotes to track time-variant energy of a biological signals and represents it in time-frequency domain. It uses the fractional ambiguity function (FAF) of signal multiplied by a suitable kernel which is designed for the biological signals generally having multi-non-stationary components. This result improves and generalizes some of the previous time-frequency distributions derived in the literature. 相似文献
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Balazs P Dörfler M Jaillet F Holighaus N Velasco G 《Journal of Computational and Applied Mathematics》2011,236(6):1481-1496
Signal analysis with classical Gabor frames leads to a fixed time-frequency resolution over the whole time-frequency plane. To overcome the limitations imposed by this rigidity, we propose an extension of Gabor theory that leads to the construction of frames with time-frequency resolution changing over time or frequency. We describe the construction of the resulting nonstationary Gabor frames and give the explicit formula for the canonical dual frame for a particular case, the painless case. We show that wavelet transforms, constant-Q transforms and more general filter banks may be modeled in the framework of nonstationary Gabor frames. Further, we present the results in the finite-dimensional case, which provides a method for implementing the above-mentioned transforms with perfect reconstruction. Finally, we elaborate on two applications of nonstationary Gabor frames in audio signal processing, namely a method for automatic adaptation to transients and an algorithm for an invertible constant-Q transform. 相似文献
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We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT. 相似文献
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周建钦 《数学的实践与认识》2009,39(24)
离散余弦变换(DCT)在数字信号、图像处理、频谱分析、数据压缩和信息隐藏等领域有着广泛的应用.推广离散余弦变换,给出一个包含三个参数的统一表达式,并证明在许多情形新变换是正交变换.最后给出一种新型离散余弦变换,并证明它是正交变换. 相似文献
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To model a non-stationary signal as a superposition of amplitude and
frequency-modulated Fourier-like oscillatory modes is important to extract information, such as the underlying dynamics, hidden in the signal. Recently, the synchrosqueezed wavelet transform (SST) and its variants have been developed to estimate instantaneous frequencies and separate the components of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST for short)
reassigns the frequency variable to sharpen the time-frequency representation and to
separate the components of a multicomponent non-stationary signal. However, FSST
works well only with multicomponent signals having slowly changing frequencies.
To deal with multicomponent signals having fast-changing frequencies, the second-order FSST (FSST2 for short) was proposed. The key point for FSST2 is to construct
a phase transformation of a signal which is the instantaneous frequency when the
signal is a linear chirp. In this paper we consider a phase transformation for FSST2
which has a simpler expression than that used in the literature. In the study the
theoretical analysis of FSST2 with this phase transformation, we observe that the
proof for the error bounds for the instantaneous frequency estimation and component recovery is simpler than that with the conventional phase transformation. We
also provide some experimental results which show that this FSST2 performs well
in non-stationary multicomponent signal separation. 相似文献
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Wavelet frames have gained considerable popularity during the past decade,primarily due to their substantiated applications in diverse and widespread fields of science and engineering.Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis.In this article,we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform.As an application,an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained. 相似文献
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The cocktail party problem deals with the specialized human listening ability to focus one's listening attention on a single talker among a cacophony of conversations and background noise. The blind source separation problem corresponds to a way to enable computers to solve the cocktail party problem in a satisfactory manner. The simplest version of spatio-temporal mixture problem, which is a type of blind source separation problems, is solved using time-frequency analysis. The analytic wavelet transform is used to represent time-frequency information and a numerical simulation is given. 相似文献
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Benjamin Ricaud Guillaume Stempfel Bruno Torrésani Christoph Wiesmeyr Hélène Lachambre Darian Onchis 《Advances in Computational Mathematics》2014,40(3):683-702
Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on l p -norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples. 相似文献