Practical Implementation of Second Generation Wavelet Transformation on 2D Images by Transformation Matrixes

Abstract

To perform second generation wavelet transformation in digital signal processing is a common operation. Most obvious way to carry out this task is by program cycle management. Computational software usually executes direct matrix algebraic operations much faster, compared to cycles. Avoiding organizing cycles, can increase the processing speed by magnitudes. This paper introduces transformation matrixes to execute the key steps of wavelet transformation: filtering and downsampling. By the employment of the described transformational matrixes, wavelet transformation and filtering of two dimensional images or discrete datasets could be easier and faster.