FFT based sign modulated DWT filter bank

Discrete Wavelet Transform (DWT) and its generalization, Wavelet Packets (WPs) have acquired central position for signal representation. DWT provides good compaction for low pass signals only. On the other hand WPs offers good approximation property for arbitrary signal but the associated computational cost of finding an optimal WP basis is quite high. In this paper, we introduce a signal conditioning based modulated wavelet transform. The proposed transformation provides better approximation performance than that offered by DWT for signal with arbitrary spectra, which can be used in signal approximation, compression, de-noising etc. The proposed transformation in its original form requires computation of signal parity information for which a fast algorithm is proposed. The proposed transform can be implemented efficiently similar to wavelet transform. Simulation results to demonstrate the improved approximation performance are also provided.