Modulated wavelet basis

DWT representation is ideally suited for low pass signals. Also, efficient algorithm exits for their implementations. To broaden their applicability to signal with arbitrary spectra signal conditioning has been introduced. Prior to each stage of DWT decomposition the signal is conditioned such that DWT provides efficient representation for that signal. This signal conditioning is an invertible process, so that conditioning doesn´t lead to any loss of signal information. Two theorems have been proposed to incorporate the signal conditioning information itself in the analysis and synthesis filters of the embedded DWT. The proposed process of conditioning and DWT decomposition is shown equivalent to a modulated DWT operating on the original signal. An expression for the resulting modulated basis is presented. Other than providing efficient representation of signal with arbitrary spectra, an added advantage is that the basis is still structured.