Analysis of error in the fixed-point implementation of two-dimensional discrete wavelet transforms

Computational error due to the fixed-point implementation of two-dimensional (2-D) discrete wavelet transform (DWT) is analyzed. This analysis is based on the exact knowledge of the DWT analysis and synthesis filters and the word length of the original image. In the fixed-point implementation, it is crucial to understand and analyze effects of finite precision in filters coefficients as well as rounding of intermediate calculations for the purpose of storage and/or transmission. Analyses and formulations are presented for both convolution and lifting approaches and they are validated by Monte Carlo simulations. The specific example used throughout this work is the lossy wavelet transformation used in the JPEG2000 compression standard.