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    Wavelet Analysis 小波分析
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    This is a module in AutoSignal

    在光譜菜單或工具欄光譜連續小波頻譜(三維曲面)選項給出了連續小波變換( CWT)在一個全3D譜格式。連續小波變換是一種多分辨率時頻技術,是探索已知的非平穩的數據是有用的。它的值也用於確定數據是否可以被安全地判斷廣義平穩所要求的很多的分光程序。

    小波

    引用Morlet ,保羅和GaussDeriv小波可用於連續小波變換頻譜分析。可調節的參數(調整後)為Morlet子是它的波數(從6到500 ) 。為保小波它是一個命令,可以從4到40 。對於高斯小波的衍生,它是衍生物(從2到80)的順序。小波通常是複雜的,但如果是複雜選中一個真正的形式都可以使用。

    可用於8964.png視圖母親小波選項來選擇小波並以圖形方式設置其屬性。

    該無機氮選項設置用於FFT的實際大小。該值與數據大小之間的差指定的零填充的量。 CWT的使用需要補零,以獲得自由的環繞效果的基於FFT的快速卷積過程。由於它往往是可能的零墊2的下一個動力,找到微不足道的環繞效果,同時達到最快的FFT性能,這是最初提出的無機氮。在頻譜的時間值的數量始終是數據計數,無論零填充。

    頻率

    該CWT提供的手段來生成使用任何一組所需頻率的小波頻譜。的全範圍產品鎖定頻率範圍從最低單位頻率的奈奎斯特頻率。如果未選中此選項,則開始和結束的頻率必須指定。

    Ln的步驟項目指定的頻率應使用對數間隔。當大多數信號的能量是在較低的頻率,這是很有用的。如果未選中此選項,則頻率間隔將是線性的。

    n個字段指定頻率的小波頻譜計數。 35默認通常給一個體面顯示,雖然它可能不足以趕上緊密間隔的低頻分量時的記錄間隔的情況下,或緊密間隔的高頻分量時的線性間距被使用。高達AutoSignal支持500個頻率。請記住,每個頻率都需要無機氮長度的單獨的FFT ,所以計算時間和大數據集的內存需求會上升明顯被指定的高頻率計數時。

    高頻率分辨率的Morlet小波

    與大型數據集(即,大小16K或更大) ,當使用高Morlet子波數可提供顯著提高頻率分辨率。這些高波數必須謹慎但可以使用,因為窄帶特性可以計算的連續小波變換的離散頻率之間完全消失。為了確保準確的分析,使用較低的Morlet子波數,一個產生顯著“模糊性”的頻率首先確定的主要光譜特徵。然後,在高波數,確保相同的密鑰光譜特徵通過使用多達500個頻率,對數標度的最大計數仍然出現,或限制頻率,以指定的感興趣頻帶。為了防止洗出的光譜信息,還需要謹慎使用過高的波數與有太少振盪或過短的採樣長度的數據。你不能overspecify小波;被分析的數據序列應具有比小波更明顯的振盪。

    較高的Morlet子波數範圍內時增加的模糊性。這可以是非常大的數據集非常有用。一百萬總樣本的數據集將有大約1000名樣本的時間為每個像素在渲染系統。與超精細的時間分辨率的小波能產生其中一個功能出現和消失完全是千個時間單位內的頻譜。在這種情況下,是用於表面繪製的平均化的抽取可能導致在時間上是丟失了這樣的局部特性。高波數Morlet小波產生足夠的模糊性在時間上表面抽取內確保正確映射。

    表面抽取

    CWT的頻譜是由評估二元B樣條插值以圖形方式呈現。權力也計算通過整合這interpolant.For性能比較的原因,並節省內存,這B樣條插值是有限的,共65536個節點。如果對重生成網格(數據尺寸x的頻度計數)與以上值的這個號碼,一個平均抽取用於減少節點的計數的插值的係數被計算之前。抽取通常不是連續小波變換光譜的一個問題,因為它是不能直接看到功率或幅度,以及平均有對功率計算的影響最小。

     

    The Continuous Wavelet Spectrum (3D Surface) option in the Spectral menu or the Spectral toolbar presents the Continuous Wavelet Transform (CWT) in a full 3D spectral format. The CWT is a multiresolution time-frequency technique that is useful for exploring data known to be non-stationary. It is also of value for determining whether data can be safely judged wide-sense stationary as required by many of the spectral procedures.

    Wavelet

    The Morlet, Paul, and GaussDeriv wavelets are available for CWT spectral analysis. The adjustable parameter (Adj) for the Morlet is its wavenumber (from 6 to 500). For the Paul wavelet it is an order that can vary from 4 to 40. For the Derivative of Gaussian wavelet, it is the order of the derivative (from 2 to 80). The wavelets are normally complex, but a real form can be used if Complex is unchecked.

    8964.png The View Mother Wavelet option can be used to select the wavelet and set its properties graphically.

    The Nmin option sets the actual size of the FFT that is used. The difference between this value and the data size specifies the amount of zero padding. The CWT uses an FFT-based fast convolution procedure that requires zero padding in order to be free of wraparound effects. Since it is often possible to zero pad to the next power of 2 and find negligible wraparound effects and also achieve the fastest FFT performance, this is the Nmin initially presented. The number of time values in the spectrum is always the data count, irrespective of zero padding.

    Frequency

    The CWT offers the means to generate a wavelet spectrum using any set of frequencies desired. The Full Range item locks the frequency range from the lowest unit frequency to the Nyquist frequency. When this option is not checked, the start and end frequencies must be specified.

    The Ln Steps item specifies that the frequencies should use a logarithmic spacing. This is useful when most of a signal's energy is at lower frequencies. When this option is not checked, the frequency spacing will be linear.

    The n field specifies the count of frequencies in the wavelet spectrum. The default of 35 usually gives a respectable coverage, although it may be insufficient to catch closely spaced low frequency components when a log spacing is used, or closely spaced high frequency components when a linear spacing is used. AutoSignal supports up to 500 frequencies. Bear in mind that each frequency requires a separate FFT of Nmin length, so computation times and memory requirements for large data sets will go up appreciably when high frequency counts are specified.

    High Frequency Resolution Morlet Wavelets

    High Morlet wave numbers can offer dramatically improved frequency resolution when used with large data sets (ie., 16K or greater in size). These high wave numbers must be used with caution, however, since narrowband features can completely vanish between the discrete frequencies computed in the CWT. To insure an accurate analysis, first identify the primary spectral features using a lower Morlet wave number, one that produces significant "fuzziness" in frequency. Then, at the high wave number, insure that the same key spectral features still appear by using up to the maximum count of 500 frequencies, logarithmic scaling, or limit the frequencies to a specified band of interest. To prevent washing out spectral information, it is also necessary to be cautious of using too high a wave number with data that have too few oscillations or too short a sampling length. You must not overspecify the wavelet; the data sequence being analyzed should have appreciably more oscillations than the wavelet.

    Higher Morlet wave numbers increase the fuzziness within time. This can be useful with very large data sets. A data set with one million total samples will have perhaps one thousand samples in time for each pixel in a rendering system. A wavelet with ultra-fine time resolution can produce a spectrum where a feature appears and disappears entirely within the one thousand time units. In such a case, the averaging decimation that is used for surface rendering may result in such local features in time being lost. A high wave number Morlet wavelet produces sufficient fuzziness in time to insure proper mapping within the surface decimation.

    Surface Decimation

    The CWT spectrum is graphically rendered by evaluating a bivariate B-spline interpolant. Powers are also computed by integrating this interpolant.For perfomance reasons and to conserve memory, this B-spline interpolant is limited to a total of 65536 nodes. If the CWT generates a grid (data size x frequency count) with more than this number of values, an averaging decimation is used to reduce the nodal count before the interpolant's coefficients are computed. The decimation is not normally a problem for CWT spectra since it is not possible to directly view power or amplitude, and the averaging has minimal impact on power computations.