The Discrete Wavelet Transform

Abstract: In this thesis we will explore the theory behind wavelets. The main focus is on the discrete wavelet transform, although to reach this goal we will also introduce the discrete Fourier transform as it allow us to derive important properties related to wavelet theory, such as the multiresolution analysis. Based on the multiresolution it will be shown how the discrete wavelet transform can be formulated and show how it can be expressed in terms of a matrix. In later chapters we will see how the discrete wavelet transform can be generalized into two dimensions, and discover how it can be used in image processing.