Wavelet packet approximation

Wavelet packet expansions have been the centre of many research problems in the last few years. We begin by furnishing few results related to approximation of functions of (Formula presented.) using wavelet packets. ‘Orthogonal Coifman wavelet packet (in short OCWP) systems’ followed by ‘biorthogonal Coifman wavelet packet (in short BCWP) systems’ with the vanishing moments distributed equally between the scaling function and the wavelet packet functions (Formula presented.) have been introduced and thereby wavelet packet approximation theorem is given. It was known earlier that, ‘Hilbert transform of wavelet is again a wavelet.’ This motivated us to seek whether ‘Hilbert transform of wavelet packets are again wavelet packets’ or not? The answer to this query has been addressed and certain results have been given in this direction. Finally, Hartley-like wavelet packets have been introduced and results by Hernández and Weiss have been generalized.