IDL Wavelet Toolkit User's Guide

82 Chapter 4: IDL Wavelet Toolkit ReferenceWV_FN_GAUSSIANSyntaxThe WV_FN_GAUSSIAN function constructs wavelet coefficients for the Gaussianwavelet function. In real space, the Gaussian wavelet function is proportional to them-th order derivative of a Gaussian, exp(–x 2 /2). The Gaussian second derivative,(x 2 –1) exp(–x 2 /2), is often referred to as the Marr wavelet.Result = WV_FN_GAUSSIAN( [Order] [, Scale, N][, /DOUBLE] [, FREQUENCY=variable] [, /SPATIAL] [, WAVELET=variable])The returned value of this function is an anonymous structure of information aboutthe particular wavelet.Tag Type DefinitionFAMILY STRING ‘Gaussian’ORDER_NAME STRING ‘Derivative’ORDER_RANGE DBLARR(3) 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 SQRT(2) [Autocorrelation e-fold distance]FOURIER_PERIOD DOUBLE Ratio of Fourier wavelength to scaleTable 4-8: Structure Tags for ResultWV_FN_GAUSSIANIDL Wavelet Toolkit