Shiftability and filter bank design using Morlet wavelet

A multi-resolution representation through wavelet transform has proved to be beneficial for many signal processing applications. For example, Morlet wavelet has shown good performance in tasks like audio coding and image enhancement. Unfortunately, wavelet transforms are unstable when the input signal is shifted in position. Prior works formalize this problem by defining a type of translation invariance called shiftability. Shiftability constraint is equivalent to the constraint that the response power of the transform in the sub-band is preserved with respect to translations of the input signal. In this paper, we propose constraints for filter bank design that guarantee shiftability. Also, we use the proposed constraints to design a filter bank that implements the Morlet wavelet transform. We use the Morlet wavelet based on the fact that it has good properties in joint time-frequency localization and it has shown approximate shiftability. The filter bank proposed presents good results with respect to shiftability.