wavMRDSum(wmtsa)
wavMRDSum()所属R语言包：wmtsa
Partial summation of a multiresolution decomposition
多分辨率分解的部分的总和
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Forms a multiresolution decomposition (MRD) by taking a specified discrete wavelet transform of the input series and subsequently inverting each level of the transform back to the "time" domain. The resulting components of the MRD form an octave-band decomposition of the original series, and can be summed together to reconstruct the original series. Summing only a subset of these components can be viewed as a denoising
形成了一个多分辨率分解（MRD）以指定的离散小波变换的输入序列和随后反相变换回的“时间”域的每个级别的。的MRD形式的一个倍频程频带分解，在原始的系列中，将得到的组件，并且可以叠加在一起来重建原始的系列。去噪求和只有一个子集，这些组件可以被看作是
用法----------Usage----------
levels=1, xform="modwt", reflect=TRUE,
参数----------Arguments----------
参数：x
a vector containing a uniformly-sampled real-valued time series.
一个向量，包含均匀采样的实值的时间序列。
参数：keep.details
a logical value. If TRUE, the details corresponding to the specified levels are included in the partial summation over the MRD components. The user also has the choice to exclude the smooth in the summation via the keep.smooth option, but one of keep.details and keep.smooth must be TRUE. Default: TRUE.
一个逻辑值。如果TRUE，包括在对应于指定的水平的细节的MRD组件的部分求和。用户还可以选择排除顺利通过keep.smooth选项，但keep.details和keep.smooth是TRUE的总和。默认值：TRUE。
参数：keep.smooth
a logical value. If TRUE, the smooth at the last decomposition level is added to the partial summation over specified details. The smooth typically contains low-frequency trends present in a series, so removing the smooth (keep.smooth=FALSE) will result in removing the trend in such cases. The user also has the choice to exclude the details in the summation via the keep.details option, but one of keep.details and keep.smooth must be TRUE. Default: TRUE.
一个逻辑值。如果TRUE，在最后的分解级别的顺利添加到指定的详细资料的部分求和。通常的顺利低频趋势中存在的一个系列，所以删除光滑（keep.smooth=FALSE）中删除的趋势，在这种情况下，将导致。用户还可以选择通过keep.details选项，但keep.details和keep.smooth是TRUE排除在总结。默认值：TRUE。
参数：levels
an integer vector of integers denoting the MRD detail(s) to sum over in forming a denoised approximation to the orginal series (the summation is performed across scale and nto across time). All values must be positive integers, and cannot exceed floor(logb(length(x),2)) if reflect=FALSE and, if reflect=TRUE, cannot exceed floor(logb((length(x)-1)/(L-1) + 1, b=2)) where L is the length of the wavelet filter. Use the keep.smooth option to also include the last level's smooth in the summation. Default: 1.
的整数向量整数表示的MRD的细节（S），总结形成去噪近似的总和跨越时间跨越规模和NTO）原价系列（。所有的值必须为正整数，且不能超过floor(logb(length(x),2))如果reflect=FALSE，如果reflect=TRUE，不能超过floor(logb((length(x)-1)/(L-1) + 1, b=2))其中L的小波滤波器的长度。使用keep.smooth选项还包括最后一个级别的，光滑的总和。默认值：1。
参数：reflect
a logical value. If TRUE, the last Lj = (2^n.level - 1)(L - 1) + 1 coefficients of the series are reflected (reversed and appended to the end of the series) in order to attenuate the adverse effect of circular filter operations on wavelet transform coefficients for series whose endpoint levels are (highly) mismatched. The variable Lj represents the effective filter length at decomposition level n.level, where L is the length of the wavelet (or scaling) filter. A similar operation is performed at the beginning of the series. After synthesis and (partial) summation of the resulting details and smooth, the middle N points of the result are returned, where N is the length of the original time series. Default: TRUE.
一个逻辑值。如果TRUE，最后Lj = (2^n.level - 1)(L - 1) + 1系列的系数被反射（扭转和所附的系列结束）为了衰减圆形的过滤操作的不利影响，小波变换系数的系列，其端点水平分别为（高度）不匹配。变量Lj有效过滤长度在分解过程中的n.level，L的小波（或缩放）滤波器的长度。在该系列的开头执行类似的操作。合成和（部分）后求和所得到的细节和光滑，中间N点的结果被返回，其中N是原始的时间序列的长度。默认值：TRUE。
参数：wavelet
a character string denoting the filter type. See wavDaubechies for details. Default: "s8".
一个字符串，表示过滤器的类型。见wavDaubechies的详细信息。默认值："s8"。
参数：xform
a character string denoting the wavelet transform type. Choices are "dwt" and "modwt" for the discrete wavelet transform (DWT) and maximal overlap DWT (MODWT), respectively. The DWT is a decimated transform where (at each level) the number of transform coefficients is halved. Given N is the length of the original time series, the total number of DWT transform coefficients is N. The MODWT is a non-decimated transform where the number of coefficients at each level is N and the total number of transform coefficients is N*n.level. Unlike the DWT, the MODWT is shift-invariant and is seen as a weighted average of all possible non-redundant shifts of the DWT. See the references for details. Default: "modwt".
一个字符串，表示小波变换的类型。选择是"dwt"和"modwt"离散小波变换（DWT）和最大重叠载重吨（MODWT），分别。 DWT是抽取转换（每级）的变换系数的数量减少了一半。鉴于N是原来的时间序列的长度，DWT的变换系数的总数目是N。的MODWT非抽取的变换系数的数目在每个级别N和变换系数的总数是N*n.level。与载重吨，的MODWT平移不变性，被视为所有可能的非冗余变化的DWT的加权平均。有关详细信息，请参考相关手册。默认值："modwt"。
Details
详细信息----------Details----------
Performs a level J decimated or undecimated discrete wavelet transform on the input series and inverts the transform at each level separately to produce details D1,...,DJ and smooth SJ. The decomposition is additive such that the original series X may be reconstructed ala X=D1 + D2 + ... DJ + SJ. As the effective wavelet filters at level j are nominally associated with approximate band pass filters, the details Dj correspond approximately to normalized frequencies on the interval [1/2^(j+1), 1/2^j], while the content of the smooth SJ corresponds approximately to normalized frequencies [0, 1/2^(J+1)]. The collection of details and smooth form a multiresolution decomposition (MRD).
执行的水平J消灭或者非抽样离散小波变换的输入序列和反转变换在每个级别分别生产细节D1,...,DJ和光滑SJ。分解添加剂等原系列X可以重建鼻翼X=D1 + D2 + ... DJ + SJ。级作为有效的小波滤波器j名义上与近似的带通滤波器，详情Dj对应约归一化频率的间隔[1/2^(j+1), 1/2^j]，而内容的顺利SJ大约相当于归一化频率[0, 1/2^(J+1)]。收集的细节和平滑的多分辨率分解（MRD）。
With the intent of removing unwanted noise events, a summation over a subset of MRD components may be calculated yielding a smooth approximation to the original series. For example, summing all MRD components beyond D1 is tantamount to a low-pass filtering of the original series (whether or not this is a relevant and sufficient noise removal technique is left to the discretion of the practitioner). This function allows the user to specify the decomposition levels they wish to sum over in order to form a multiresolution approximation. The inclusion of the last level's smooth in the summation is controlled by the optional keep.smooth argument.
的意图，消除不必要的噪音事件，求和，可以计算在MRD的组件的一个子集产生一个光滑逼近原始的系列。例如，总结MRD组件超出D1无异于一个低通滤波原始的系列（这是否是相关的和足够的噪声消除技术，剩下的自由裁量权的医生）。此功能允许用户指定他们希望总结，从而形成一个多分辨率近似的分解水平。包含了可选的的keep.smooth参数控制的最后一个级别的光滑的总和。
The user may also select either a decimated wavelet transform (DWT) or an undecimated wavelet transform (MODWT). However, we recommend that the user stick with the MODWT for the following reasons:
用户也可以选择一个抽取小波变换（DWT）或抽样小波变换（MODWT）。但是，我们建议用户棒的MODWT，原因如下：
Translation invarianceUnlike the DWT, the MODWT is translation invariant, meaning that a (circular) shift of the input series will result in a corresponding (circular) shift of the transform coefficients.
翻译invarianceUnlike载重吨，MODWT是平移不变，这意味着输入系列（圆形）转变将导致在相应的（循环）移位变换系数。
SmoothnessThe MODWT coefficients are a result of cycle-spinning, where averages are taken over all unique DWTs resulting from various circular shifts of the original series. The resulting MODWT MRD is relatively more smooth than the corresponding DWT MRD.
SmoothnessThe MODWT系数是由于纺周期的平均值，其中产生的各种圆形原系列的变化都是独一无二的载重吨接管的。 MODWT MRD相应的DWT MRD相对比较流畅。
Zero phase aligmentUnlike the DWT MRD, the MODWT MRD produces components that are associated with exactly zero phase filter operations such that events (such as peaks) in the details and smooth line up exactly with those of the original series.
零的阶段aligmentUnlike DWT MRD，MODWT MRD生产零部件，都与精确的零相位滤波器的操作，这样在细节和流畅的线条，正好与原始的系列的事件（如峰）。
Computational speedThe DWT is faster than the MODWT, but the MODWT is still quite fast, requiring multiplication and summation operations on the same order as the popular Fast Fourier Transform.
计算speedThe的DWT的速度比MODWT，但的MODWT还是蛮快的，需要的乘法和累加操作上流行的快速傅立叶变换的顺序相同。
值----------Value----------
a vector containing the denoised series.
一个向量，包含去噪系列。
参考文献----------References----------
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
T.W. Randolph and Y. Yasui, Multiscale Processing of Mass Spectrometry Data, Biometrics, 62:589–97, 2006.
参见----------See Also----------
实例----------Examples----------
## create a MODWT-based MRD of the sunspots series [太阳黑子系列＃创建一个基于一个MODWT的的MRD]
## and sum over decomposition levels 4 to 6 [＃总和超过层层分解4~6]
x <- as.vector(sunspots)
z1 <- wavMRDSum(x, levels=4:6)
stackPlot(x=as.vector(time(sunspots)),
y=list(sunspots=x, "D4+D5+D6"=z1),
ylim=range(x,z1))
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
注3：如遇到不准确之处，请在本贴的后面进行回帖，我们会逐渐进行修订。
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发表于 2012-10-1 22:55:57
