Anatomy of Haar Wavelet Filter and Its Implementation for Signal Processing

This paper gives an insight to the workings of discrete wavelet transformation (DWT) in context of education, with the objective to integrate teaching and research by promoting signal processing and control as a field that embraces science, technology, engineering and mathematics (STEM). In more detail, this contribution showcases a possible lecture structure of the basic principle of orthogonal wavelets in general, and the discrete wavelet decomposition method. The architecture of the presented software structure are described step-by-step, to provide an elementary guideline for a possible implementation into an embedded system. Herein, the focus is set on the Haar wavelet specifically, thus as an illustrative example, the code for the use of it is presented. With the wavelet packet transform as a method of discrete wavelet transform, the algorithm is able to decompose and reconstruct an input signal with reduction of noise. The noise of a sequence can be located, so that the wavelet basis can be rearranged. In particular, this allows for the elimination of any incoherent parts that make up the unavoidable measuring noise of the acquired signal, which was tested in GNU Octave and MATLAB®.