基于小波变换平滑主成分分析

小波变换具有很强的信号分离能力,很容易把随机噪音从信号中分离出来,从而提高信号的信噪比。本文把小波变换引入到因子分析中,提出了基于小波变换平滑主成分分析,该算法既保留普通主成分分析的正交分解,又具备了小波变换的信号分离能力。模拟数据和实验数据的结果表明,该算法具有从低信噪比的数据中提取出有用信息,并提高信号的信噪比。迭代目标变换因子分析处理实验数据的结果表明,基于小波变换平滑主成分分析的处理结果优     

红外光谱数据的小波压缩和重建

介绍了小波变换及多分辨分析理论，并利用Ｄａｕｂｅｃｈｉｅｓ的正交紧支集小波基和Ｍａｌｌａｔ算法实现了对红外光谱数据的压缩和重建。计算表明，即使对原始数据压缩５倍，仍能很好地重建原有图谱，重建光谱数据与原始光谱数据之间的均方差为０．２６０。这为光谱数据的存储、检索和处理带来了方便。     

基于小波理论的化学谱图数据自适应滤波方法研究

运用小波理论,利用噪声与真实信号小波变换极大模性态之间的显著差异,提出了一类新的化学谱图数据自适应滤波算法,从根本上突破了现有算法均依据信噪频率特性进行滤波的传统模式.经大量色谱谱图数据处理试验证明,这种算法具有无需设置初始参数,消除人为误差因素对分析计算结果的影响,信噪分离性能好及峰位和峰高保持不变等一系列优点,其鲁棒性、自适应性和谱峰保真度完全符合仪器分析信号处理的要求.     

小波变换方法的比较──红外光谱数据压缩

介绍了小波变换和多分辨分析的基本理论以及常用小波变换压缩数据的3种方法:(1)只保留模糊信号;(2)全部保留模糊信号及锐化信号中的较大值;(3)保留模糊信号及锐化信号中的较大值.将紧支集小波和正交三次B-样条小波压缩4-苯乙炔基-邻苯二甲酸酐的红外光谱数据进行了对比,计算表明正交三次B-样条小波变换方法效果较好,而在全部保留模糊信号及只保留锐化信号中数值较大的系数时,压缩比大而重建光谱数据与原始光谱数据间的均方差较小.     

用四种离散变换主组分回归方法分辨重叠吸收光谱

将离散小波变换、小波包变换、傅里叶变换和离散余弦变换与主组分回归方法结合构成4种离散变换主组分回归方法,编制了离散变换主组分回归方法的计算程序。将离散变换主组分回归方法用于处理对硝基甲苯、对硝基酚和对硝基苯胺混合物的重叠紫外吸收光谱数据。结果表明,离散变换主组分回归方法优于主组分回归方法,试样质量浓度的预测值与实际值的相对预测标准误差由3.81%降至约1.11%。     

能量色散X射线荧光光谱背景扣除方法的探讨

能量色散X射线荧光分析使得特征X射线的全能峰叠加在背景之上,针对能量色散X射线荧光谱线背景扣除算法的研究,简述了剥峰法和小波变换法扣除背景的原理,并将这两种方法用于对实际谱线的处理,取得了良好的效果.同时对两种方法的算法和处理效果进行了对比研究,表明剥峰法相对简单,而小波变换法需要考虑小波基和分解层次等的影响,但是对整个谱线的综合处理效果相对要好一些.     

小波变换与分析化学信号处理

介绍了小波变换的基本理论并对小波变换的常用算法和应用进行了评述。由于小波变换的时2频局部化性质, 使其成为信号处理的强有力工具。在分析化学领域中, 小波变换在流动注射分析、伏安分析、高效液相色谱、红外光谱、质谱、核磁共振谱、可见-紫外光谱、光声光谱、扩展X-射线吸收精细结构(EXAFS) 谱等分析化学信号的平滑滤噪、数据压缩、重叠信号解析等方面都有成功的应用。     

小波包分析-减法聚类-RBF网络同时测定痕量铁、锰

提出一种解析分光光度吲时测定数据的小波色分析-减法聚类-RBF刚络新方法。该方法用小波包分析处理吸收光潜数据,滤除信号中的噪声;采用基于山峰函数的减法聚类算法,按照自适应聚类的结果构成预测各未知样的校正集,实现校准模型的优化;由此,使RBFM络在对未知样预测时能更有效地提取光潜数据中的特征信息,提高预测结果的准确性把该算法用于模拟汽油中铁、锰合成样预测,计算表明,该方法可以显著降低测定结果的相对误差,预测结果令人满意。     

基于小波变换动态时间规整的近红外光谱模型传递方法

为解决因测量环境及仪器差异而导致的近红外光谱模型通用性较差的不足,提出一种基于小波变换动态时间规整算法的模型传递方法(Wavelet transform combined with dynamic time warping,WDTW),从而实现不同仪器之间模型的共享。首先,该方法将光谱进行小波变换预处理,然后利用动态时间规整算法(Dynamic time warping,DTW)找到近红外光谱波长点之间最优的对应关系并建立回归方程。使用近红外药品光谱数据集和汽油数据集建立传递模型,验证了基于小波变换动态时间规整模型传递方法的有效性。汽油光谱数据集C7、C8、C9和C10成分的预测标准偏差(SEP)分别为0.414 4、0.801 1、1.090 4和1.290 8;药品光谱数据集活性、硬度和重量的SEP分别为2.585 6、0.434 5和2.270 3,均小于传统方法。上述实验结果表明,所建立的模型传递方法能有效消除源机光谱和目标机光谱之间的差异,提高模型的稳定性和准确性,实现模型传递的效果。     

连续小波变换-独立成分回归算法及其在多组分分析中的应用

采用连续小波变换（CWT）对光谱数据进行处理，用独立成分分析（ICA）进行特征提取，再用回归分析方法对被测组分进行测定，建立了连续小波变换一独立成分回归（CWT-ICR）方法。方法用于肉样品中水分、脂肪和蛋白质多组分的同时测定，所得结果与化学法测得结果相符。     

去卷积伏安法中离散数据处理的方法研究(Ⅰ)──正交小波变换平滑

一系列的离散数据处理方法已成为化学计量学的重要组成部分[1],去卷和伏安法就是结合计算机技术的新一代电分析方法,其激励信号与输出信号均为计算机发生和采集的数字信号,对采集到的信号一般采用移动平均法[2]和Fourier变换处理法[3]进行平滑处理．但是,Fourier变换在电分析化学领域的难度较大,运算复杂,为此,Aubarel等[4]提出了不用FFT的Fourier变换平滑算法,但是该法要先对信号进行预处理,并且对Fourier的和式要反复进行折叠,计算量较大．80年代末发展起来的小波变换引起了人们广泛的关注[5],被称为数学“显微镜”,具有…     

A Differential Method Based on Spline Wavelet Transform

Wavelet Transform (WT), which develops from Fourier transform, is a new signal processing technique. It is of time and frequency domain localization properties.     

分析化学计量学中的新方法─—小波分析

小波分析在分析信号处理中具有诸多显著的优点。本文介绍了小波分析的一般描述，综述了化学计量学在的小波新方法，并展望了小波分析在分析化学计量学中的应用前景。     

新极谱法实验数据的富里叶变换平滑

本文提出一种新的富里叶变换平滑算法并应用于处理阶梯扫描伏安法的实验数据。方法的建立主要是基于平滑原理的缩减步骤、三角函数周期性及和角公式计算正弦、余弦的简化方法。本法对新极谱法实验数据的处理较最小二乘多项式拟合平滑效果更显著。     

Practical aspects of Fourier transform and correlation based processing of spectrochemical data

Fourier transform based signal processing methods are beginning to be widely used for the treatment of spectrochemical data. The most common approach to Fourier transformation is through the utilization of the so called Fast Fourier Transform algorithm or FFT as it is usually designated. However, several versions of the FFT abound in the literature and in program libraries and many subtleties exist with respect to data pre-treatment, data post-treatment, inverse Fourier transformation and manipulation of real and imaginary arrays that can cause considerable grief to the uninitiated. In this presentation numerous examples will be presented illustrating several practical aspects of implementing FFT's and cross-correlations (Fourier transform route) on spectrochemical data sets. Particular attention is paid to the manipulation to the input and output real and imaginary arrays.     

Filtering and integration of chromatographic data: a tool to improve calibration?

The effect of filtering and automated integration of chromatographic data on the calibration curve and detection limit was assessed. In a first approach simulated chromatograms were used to quantify the effects of data processing. Three types of filters were used: Savitzky-Golay, Fourier and Wavelet filter. The filter parameters chosen have been optimized in a previous study. The simulated data have been integrated by a commercial software package. The use of applying the DIN 32645 concept for the determination of the detection limit of chromatographic data is discussed and opposed to the concept of the method detection limit. Under the conditions investigated, filtering can improve the limit of detection up to a factor of three. This can be explained by the fact that filtering reduces the variance of the peak area and height and the limit of detection is mainly determined by their variance. However, the integration algorithm practically limits the possible improvements by filtering the data.     

Automated charge state determination of complex isotope-resolved mass spectra by peak-target Fourier transform

This study describes a new algorithm for charge state determination of complex isotope-resolved mass spectra. This algorithm is based on peak-target Fourier transform (PTFT) of isotope packets. It is modified from the widely used Fourier transform method because Fourier transform may give ambiguous charge state assignment for low signal-to-noise ratio (S/N) or overlapping isotopic clusters. The PTFT algorithm applies a novel "folding" strategy to enhance peaks that are symmetrically spaced about the targeted peak before applying the FT. The "folding" strategy multiplies each point to the high-m/z side of the targeted peak by its counterpart on the low-m/z side. A Fourier transform of this "folded" spectrum is thus simplified, emphasizing the charge state of the "chosen" ion, whereas ions of other charge states contribute less to the transformed data. An intensity-dependent technique is also proposed for charge state determination from frequency signals. The performance of PTFT is demonstrated using experimental electrospray ionization Fourier transform ion cyclotron resonance mass spectra. The results show that PTFT is robust for charge state determination of low S/N and overlapping isotopic clusters, and also useful for manual verification of potential hidden isotopic clusters that may be missed by the current analysis algorithms, i.e., AID-MS or THRASH.     

Wavelet transform for Shah convolution velocity measurements of single particles and solutes in a microfluidic chip

Wavelet transform analysis is applied to determine the speed of fluorescent polystyrene microspheres and fluorescent solutes in a microchip. The data analysed consist of the periodical signal (Shah convolution) obtained when fluorescent particles or solute plugs move in a channel that is covered with a chromium grid pattern. This setup converts velocity into a (fluorescence emission) frequency, and previous analyses therefore used Fourier transform to extract the frequency information. In this paper it is shown that wavelet transform has some advantages over Fourier transform. With wavelet transform, time information can be obtained in addition to frequency information. Thus the speed of individual particles was determined together with their moments of appearance and disappearance in the system. With solutes small changes of velocity during the analysis were detected, and an improvement in peak frequency resolution was obtained.     

Wavelet transform-based Curve Fitting

Curve fitting methods are now widely applied both qualitative and quantitatively to separate overlapping peaks in composite profiles. Nevertheless, the achievement of a good representative fit requires the knowledge of five parameters:the number of component bands, their positions, shapes and widths, and the form of the baseline. Clearly, curve fitting is considerably facilitated if approximate values for some of the parameters are known at the outset. Up to present, there are many methods employed for improving the curve-fitted conditions^[1,2]. Wavelet transform is a high performance signal processing technique developed from the Fourier transform.     

Wavelet transform-based Fourier deconvolution for resolving oscillographic signals

Fourier self-deconvolution is an effective means of resolving overlapped bands, but this method requires a mathematical model to yield deconvolution and it is quite sensitive to noises in unresolved bands. Wavelet transform is a technique for noise reduction and deterministic feature capturing because its time-frequency localization or scale is not the same in the entire time-frequency domain. In this work, wavelet transform-based Fourier deconvolution was proposed, in which a discrete approximation (such as A(2)) obtained from performing wavelet transform on the original data was substituted for the original data to be deconvolved and another discrete appropriate approximation (such as A(5)) was used as a lineshape function to yield deconvolution. Again, instead of the apodization function, the B-spline wavelet was used to smooth the deconvolved data to enhance the signal-to-noise ratio. As a consequence, this method does not suffer as badly as Fourier self-deconvolution from noises in the original data. Thus, resolution enhancement can be increased significantly, especially for signals with higher noise level. Furthermore, this method does not require a mathematical model to yield deconvolution; it is very convenient to deconvolve electrochemical signals.