2-band discrete wavelet transform (DWT)

Dual-Tree Complex Wavelet Packet-The 2-band discrete wavelet transform (DWT) provides

an octave-band analysis in the frequency domain, but this

might not be ‘optimal’ for a given signal. The discrete wavelet

packet transform (DWPT) provides a dictionary of bases over

which one can search for an optimal representation (without

constraining the analysis to an octave-band one) for the signal

at hand. However, it is well known that both the DWT and the

DWPT are shift-varying. Also, when these transforms are extended

to 2-D and higher dimensions using tensor products, they

do not provide a geometrically oriented analysis. The dual-tree

complex wavelet transform (DT-CWT), introduced by Kingsbury,

is approximately shift-invariant and provides directional analysis

in 2-D and higher dimensions. In this paper, we propose a method

to implement a dual-tree complex wavelet packet transform (DTCWPT),

extending the DT-CWT as the DWPT extends the DWT.

To find the best complex wavelet packet frame for a given

signal, w