Quantification of Finite Word Length Effects in Filter Banks and Wavelet Transform

Abstract

It is known that computers store numbers not with infinite precision but rather in some approximation that can be packed into a fixed number of bits, and this leads to loss of information. Present work studies the effect of loss of information on the response of filter banks and Wavelet transform. These effects are universally called Finite word length effects. There are number of effects of finite word length like overflow and truncation errors in addition, and multiplication, effects of coefficient quantization, limit cycle, etc. Present focus is on coefficient quantization. To see Finite word length effects in filter banks and Wavelet transform authors have used algorithm in which image has been first wavelet transformed and again constructed back using quantized coefficients. Pyramidal algorithm with DAUB4 wavelet has been used. Simulation for both direct quantization of DAUB4 coefficients and equivalent lattice coefficients quantization has been performed. All simulations are done in C.