IDL Wavelet Toolkit User's Guide

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74 Chapter 4: IDL Wavelet Toolkit ReferenceWV_DWTThe WV_DWT function returns the multi-dimensional discrete wavelet transform ofthe input Array. The transform is done by WV_PWT using a user-inputted waveletfilter.The length of each dimension of Array must be either a power of two (2), or must beless than four (4). The transform is not computed over dimensions of lengths less thanfour (4), but is computed over all other dimensions (for example, the wavelettransform of an array of size [3, 256] is computed over each [1, 256] column vector).WV_DWT is based on the routine wtn described in section 13.10 of NumericalRecipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press),and is used by permission.SyntaxResult = WV_DWT(Array, Scaling, Wavelet, Ioff, Joff [, /DOUBLE] [, /INVERSE][, N_LEVELS=value])Return ValueThe result is an output array of the same dimensions as Array, containing the discretewavelet transform over each dimension.ArgumentsArrayThe input vector or array. The length of each dimension must be either less than four(4) or a power of two (2).ScalingA vector of scaling (father) coefficients, of length N.WaveletA vector of wavelet (mother) coefficients, of length N.WV_DWTIDL Wavelet Toolkit
Chapter 4: IDL Wavelet Toolkit Reference 75IoffJoffAn integer that specifies the support offset for Scaling. To center the scaling functionover each point in Array, set Ioff to –N/2+2.An integer that specifies the support offset for Wavelet. To center the waveletfunction over each point in Array, set Joff to –N/2+2.KeywordsDOUBLESet this keyword to force the computation to be done in double-precision arithmetic.INVERSEIf set, the inverse transform is computed. By default, the forward transform iscomputed.N_LEVELSSet this keyword to the number of wavelet levels to compute in the pyramidalgorithm, starting with the smallest wavelet scale and progressing to larger scales. Ifthis keyword is not set or is set to zero, then all wavelet levels in the pyramidalgorithm are computed.Method and Result FormatThe WV_DWT function computes the wavelet coefficients using the pyramidalalgorithm (Mallat 1989).One-Dimensional VectorFor a one-dimensional vector, the pyramid appears below:Array elements[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\ / \ / \ / \ / \ / \ / \ / \ /s0,d0 s1,d1 s2,d2 s3,d3 s4,d4 s5,d5 s6,d6 s7,d7\ / \ / \ / \ /\ / \ / \ / \ /S0,D0 S1,D1 S2,D2 S3,D3\ / \ /\ / \ /IDL Wavelet ToolkitWV_DWT
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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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Chapter 2: Using the IDL Wavelet To
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IDL Wavelet Toolkit User's Guide

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