Daubechies Wavelet - Implementation

Implementation

While software such as Mathematica supports Daubechies wavelets directly a basic implementation is simple in MATLAB (in this case, Daubechies 4). This implementation uses periodization to handle the problem of finite length signals. Other, more sophisticated methods are available, but often it is not necessary to use these as it only affects the very ends of the transformed signal. The periodization is accomplished in the forward transform directly in MATLAB vector notation, and the inverse transform by using the circshift function: