Fourier, block, and lapped transforms

Development of two types of lapped transforms including, lapped orthogonal transform (LOT) and modulated lapped transform (MLT) from standard block transforms as a starting point is presented. The Fourier transform and its related discrete transforms are of great importance in both theory and practice of signal and image processing, as it allows to describe both signal and system properties and the relation between system output signals in the frequency domain. The discrete Fourier transform (DFT) represents a discrete-time signal of finite length by a finite number of discrete-frequency coefficients. Lapped transforms aim at reducing or even eliminating block artifacts by the use of overlapping basis functions, which extend over more than one block.