Extended lapped transforms with linear phase basis functions and perfect reconstruction

In this paper we introduce the theory and design of a new class of Extended lapped transform with basis functions having linear phase property and perfect reconstruction. Lapped Transforms are powerful tools for signal, image and video processing applications. The Extended Lapped transform reported previously in the literature is a modulated lapped transform. Even though they provide efficient implementation the basis functions do not have the linear phase property. This property is crucial in image coding applications at low bit rates. Linear phase property not only eliminates phase distortion but also permit use of simple symmetric extension methods to accurately handle boundaries of the finite length signals. Furthermore linear phase property leads to more efficient implementation. The formulation is based on type II Discrete Cosine Transform (DCT II). Hence it has fast and efficient structure. The necessary and sufficient conditions for Perfect Reconstruction and linear phase are derived.