On the design of orthonormal wavelets for finite-length signals

We describe a procedure for designing compactly supported orthonormal wavelets for finite-length wavelet transform. The designed wavelets yield perfect reconstruction with a more general class of signal extensions, including symmetric extension and zero-padding, rather than the common periodic extension. This combines the compact representation from orthonormal wavelets with the good behaviour at the borders from smooth extensions, which enables their use in signal coding. We show few examples that illustrate the improvement for coding finite-length signals.