Appendix B

APPENDIX C

Appendix D

C.1. INTRODUCTION

Multi-frequency decomposition schemes and subband coding have come a long way over the years. Actually Crochiere, Webber and Flanagan introduced them in 1976 for speech signals with the basic idea to decompose the input signal into a number of frequency bands using a bank of band pass filters; in the same year Croisier, Esteban and Galand introduced the Quadrature Mirror Filters to allow alias-free reconstruction of the signals. Vetterly in 1984 extended the application of QMF to two-dimensional and multi-dimensional signals; subsequently Woods and O’Neil in 1986 presented the first image coder using subband coding and Differential Pulse Code Modulation, whereas Gharavi and Tabatabai in 1988 proposed another subband coding scheme using unequal-sized subbands. Since then a variety of subband coders capable of high quality encoding at low bit rates have emerged; a good number of multiresolution approximation schemes emerged independently. However wavelet theory, mainly discrete wavelet transform, has been recognised as a unifying framework.