![]() ![]() This pattern is discussed on the web page A Linear Algebra View of the Wavelet Transform. The index i is incremented by two with each iteration, and new scaling and wavelet function values are calculated. The equations are shown below:Įach iteration in the wavelet transform step calculates a scaling function value and a wavelet function value. ![]() The scaling and wavelet functions are calculated by taking the inner product of the coefficients and four data values. In the ordered wavelet transform the wavelet values are stored in the upper half of teh N element input vector. If the original data set has N values, the wavelet function will be applied to calculate N/2 differences (reflecting change in the data). ![]() The wavelet function coefficient values are:Įach step of the wavelet transform applies the wavelet function to the input data. In the ordered wavelet transform the smoothed values are stored in the lower half of the N element input vector. If the original data set has N values, the scaling function will be applied in the wavelet transform step to calculate N/2 smoothed values. The scaling function coefficients areĮach step of the wavelet transform applies the scaling function to the the data input. The Daubechies D4 transform has four wavelet and scaling function coefficients. The Daubechies wavelet transform is named after its inventor (or would it be discoverer?), the mathematician Ingrid Daubechies. ![]()
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