IDL Wavelet Toolkit User's Guide

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86 Chapter 4: IDL Wavelet Toolkit ReferenceArgumentsOrderA scalar that specifies the order number for the wavelet. The default is 1.ScalingOn output, contains a vector of double-precision scaling (father) coefficients.WaveletIoffJoffOn output, contains a vector of double-precision wavelet (mother) coefficients.On output, contains an integer that specifies the support offset for Scaling.On output, contains an integer that specifies the support offset for Wavelet.NoteIf none of the above arguments are present then the function will simply return theResult structure using the default Order.KeywordsNone.ReferenceDaubechies, I., 1992: Ten Lectures on Wavelets, SIAM.Version History5.3 IntroducedSee AlsoWV_DWT, WV_FN_COIFLET, WV_FN_DAUBECHIES, WV_FN_SYMLETWV_FN_HAARIDL Wavelet Toolkit
Chapter 4: IDL Wavelet Toolkit Reference 87WV_FN_MORLETSyntaxThe WV_FN_MORLET function constructs wavelet coefficients for the Morletwavelet function. In real space, the Morlet wavelet function consists of a complexexponential modulated by a Gaussian envelope: π –1/4 s –1/2 exp[i kx/ s] exp[–(x / s) 2 /2], where s is the wavelet scale, k is a non-dimensional parameter, and x is theposition.Result = WV_FN_MORLET( [Order] [, Scale, N] [, /DOUBLE][, FREQUENCY=variable] [, /SPATIAL] [, WAVELET=variable])Return ValueThe returned value of this function is an anonymous structure of information aboutthe particular wavelet.Tag Type DefinitionFAMILY STRING ‘Morlet’ORDER_NAME STRING ‘Parameter’ORDER_RANGE DBLARR(3) [3, 24, 6] Valid orders [first, last, default]ORDER DOUBLE The chosen OrderDISCRETE INT 0 [0=continuous, 1=discrete]ORTHOGONAL INT 0 [0=nonorthogonal, 1=orthogonal]SYMMETRIC INT 1 [0=asymmetric, 1=symm.]SUPPORT DOUBLE Infinity [Compact support width]MOMENTS INT 1 [Number of vanishing moments]REGULARITY DOUBLE Infinity [Number of continuous derivatives]E_FOLDING DOUBLE SQRT(2) [Autocorrelation e-fold distance]FOURIER_PERIOD DOUBLE Ratio of Fourier wavelength to scaleTable 4-10: Structure Tags for ResultIDL Wavelet ToolkitWV_FN_MORLET
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Chapter 1: Introduction to the IDL
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Chapter 2Using the IDL WaveletToolk
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