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Wavelet packets (WPs) offer a general framework for representing an arbitrary signal efficiently. But the associated computational cost of finding an optimal WP basis is quite high. To address this problem, the authors introduce, first, a signal-conditioning-based spectral density-driven wavelet transform (SDDWT). The structure of implementing SDDWT is similar to that of discrete wavelet transform (DWT) but it provides better approximation performance than that offered by DWT for a dominantly band-pass signal, including low pass. Then, for arbitrary signal, a generalisation of SDDWT, which the authors call as spectral density-driven wavelet packet (SDDWP) transform is introduced. The resultant bands have certain priority according to their ability to reduce the reconstruction error. The SDDWP can be considered a near-optimal WP basis but is also amenable to fast optimal WP basis search, at much reduced computational cost. Also, it not only provides improved approximation performance but in this case the complexity of implementing the transformation can be controlled. A side effect of the proposed transformation is the computation of signal-conditioning information, for which an efficient algorithm is provided. Simulations results have shown improved approximation performance.