Shift variance behavior for different sub - band coding systems , Biorthogonal , Orthogonal and Bspline wavelets

Sub-band coding has long been utilized and adopted in different compression, coding and reconstruction techniques in most signal processing applications. It has wide applications in communications, bit rate codec’s, sampling, and compression for images, videos and speech. However sub-band coding systems in general suffer from a certain amount of shift variance of the output reconstructed signal, due to the frequency overlap between different sub-bands in the analysis stage. This overlap is known as non-ideal anti-aliasing. In this paper we simplify the shift variance analysis of sub-band coding systems in general, and we present different metrics that have been reported in the literature to measure the bounds of shift variance for Perfect Reconstruction (PR) sub-band systems, we simplify its mathematical analysis and illustrate with graphs the reasons for these bounds and compare them. We apply these metrics on Biorthogonal, Orthogonal and Bspline wavelets and present the worst case scenario for different input signals in terms of shift variance for all these sub-band coding systems, both numerically and graphically. We finally compare the shift variance behavior for different sub-band PR systems for different types of input signals.