) Help ri1 e Edit View Go Web置 indow且e1p Find in page Wavelet ToolboxWavelets:ANewTool for SignalAnalysis:Shifting Add to Favorites Wavelet Toolbox shifting Shifting a wavelet simply means delaying (or hastening) its onset. Mathematically, delaying a functionf(t)by k is represented byf(t-k) Wavelet function Shifted wavelet function 屮(t) y(t-k) caling Five Easy Steps to a Continuous wavelet Transform Matlab6 matlab6 help/helptoolbox wavelet/cho1 113. html
区 File Edit Yiew Go Web Window Help 回4+昌 Find in page WaveletToolbox Wavelets: ANew Tool for Signal Analysis: Five Easy Steps to a Continuous Wavelet Transform g Add to Favorites Wavelet Toolbox Five Easy Steps to a Continuous Wavelet Transform The continuous wavelet transform is the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet. This process produces wavelet coefficients that are a function of scale and position It's really a very simple process. In fact, here are the five steps of an easy recipe for creating a cwt 1. Take a wavelet and compare it to a section at the start of the original signal 2. Calculate a number, C, that represents how closely correlated the wavelet is with this section of the signal. The higher c is, the more the similarity. More precisely, I the signar energy and the wavelet energy are equal to one c may be interpreted as a correlation coeffcient. Note that the results will depend on the shape of the wavelet you choose Signal Wavelet c=00102 Ready
区 File Edit Yiew Go Web Window Help 回◆ψ+舀 Find in page WaveletToolbox Wavelets:A New Tool for Signal Analysis: Five Easy Steps to a Continuous Wavelet Transform d to Favorites 3. Shift the wavelet to the right and repeat steps 1 and 2 until youve covered the whole signal Signal 4. Scale(stretch) the wavelet and repeat steps 1 through 3 Wavelet 5. Repeat steps 1 through 4 for all scales When you're done you'll have the coefficients produced at different scales by different sections of the signal. The coefficients constitute the results of a regression of the original signal performed on the wavelets
珍Hp 回x File Edit View Go Web Window Help 回4妙+舀 Find in page Wavelet Toolbox Wavelets: A New Tool for Signal Analysis: Five Easy Steps to a Continuous w: Add to Favorites How to make sense of all these coefficients? You could make a plot on which the x-axis represents position along the signal (time), the yaxis represents scale, and the color at each x-y point represents the magnitude of the wavelet coefficient C. These are the coefficient plots generated by the graphical tools Larg Coefficients 23 Smal 035∠0∠0列4|00455∠200 Coefficients
回区 File Edit View Go Web Window Help 回◆妙+舀 Wavelet Toolbox Wavelets: A New Tool for Signal Analysis: Five Easy Steps to a Continuous w: Add to Favorites These coefficient plots resemble a bumpy surface viewed from above. If you could look at the same surface from the side, you might see something like this The continuous wavelet transform coefficient plots are precisely the time-scale view of the signal we referred to earlier. It is a different view of signal data than the time- frequency Fourier view, but it is not unrelated 白 Shifting Scale and Frequency