Wavelets and filter banks: relationships and new results

The discrete version of the wavelet transform, which has recently emerged as a powerful tool for nonstationary signal analysis is closely related to filter banks, which have been studied in digital signal processing. Also, multiresolution signal analysis has been used in image processing. The relationship between these techniques is indicated. It is shown how to construct biorthogonal systems with linear-phase finite impulse response (FIR) filters and with regular analysis and synthesis. Some examples of practical interest are given. The complexity of the discrete wavelet transform is also discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>