IDL Wavelet Toolkit User's Guide

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90 Chapter 4: IDL Wavelet Toolkit ReferenceWV_FN_PAULSyntaxThe WV_FN_PAUL function constructs wavelet coefficients for the Paul waveletfunction. In real space, the Paul wavelet function is proportional to the complexpolynomial (1 – i x / s)^(–m–1), where s is the wavelet scale, m is a non-dimensionalparameter, and x is the position.Result = WV_FN_PAUL( [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 ‘Paul’ORDER_NAME STRING ‘Parameter’ORDER_RANGE DBLARR(3) [1, 20, 4] 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 continuousderivatives]E_FOLDING DOUBLE 1/sqrt(2) [Autocorrelation e-fold distance]FOURIER_PERIOD DOUBLE Ratio of Fourier wavelength to scaleTable 4-11: Structure Tags for ResultWV_FN_PAULIDL Wavelet Toolkit
Chapter 4: IDL Wavelet Toolkit Reference 91ArgumentsOrderA scalar that specifies the non-dimensional order for the wavelet. The default is 4.ScaleNA scalar that specifies the scale at which to construct the wavelet function.An integer that specifies the number of points in the wavelet function. For Fourierspace (SPATIAL=0), the frequencies are constructed following the FFT convention:• For N even: 0, 1/N, 2/N, ..., (N–2)/(2N), 1/2, –(N–2)/(2N), ..., –1/N.• For N odd: 0, 1/N, 2/N, ..., (N–1)/(2N), –(N–1)/(2N), ..., –1/N.For real space (/SPATIAL), the spatial coordinates are –(N–1)/2...(N–1)/2.NoteIf none of the above arguments are present then the function will simply return theResult structure using the default Order.KeywordsDOUBLESet this keyword to force the computation to be done in double-precision arithmetic.FREQUENCYSet this keyword to a named variable in which to return the frequency array used toconstruct the wavelet. This variable will be undefined if SPATIAL is set.SPATIALSet this keyword to return the wavelet function in real space. The default is to returnthe wavelet function in Fourier space.WAVELETSet this keyword to a named variable in which to return the wavelet function.IDL Wavelet ToolkitWV_FN_PAUL
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IDL WaveletToolkit User’sGuideIDL
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ContentsChapter 1Introduction to th
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Chapter 1Introduction to the IDLWav
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Chapter 1: Introduction to the IDL
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Chapter 1: Introduction to the IDL
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Chapter 2Using the IDL WaveletToolk
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IDL Wavelet Toolkit User's Guide

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