Abstract
The lack of translation invariance of typical real-valued discrete wavelet transforms is always pointed out as the serious problem in using them for signal and image processing. In this paper, we prove the useful theorem for considering this problem in the frequency domain. This theorem is generalized from the perfect translation invariance theorem, which gives the condition of the perfect translation invariance for complex discrete wavelet transforms of an arbitrary complex-valued square integrable function. Next, based on this theorem, we propose a new type of real-valued tight wavelet frame having perfect translation invariance.
