Wavelet packet decomposition

Wavelet packet decomposition (WPD) (sometimes known as just wavelet packets) is a wavelet transform where the signal is passed through more filters than the DWT.

In the DWT, each level is calculated by passing the previous approximation coefficients through a high and low pass filters. However in the WPD, both the detail and approximation coefficients are decomposed.

Wavelet Packet decomposition over 3 levels

For n levels of decomposition the WPD produces 2ⁿ different sets of coefficients (or nodes) as opposed to (n + 1) sets for the DWT. However, due to the downsampling process the overall number of coefficients is still the same and there is no redundancy.

From the point of view of compression, the standard wavelet transform may not produce the best result, since it is limited to wavelet bases that increase by a power of two towards the low frequencies. It could be that another combination of bases produce a more desirable representation for a particular signal. The best basis algorithm by Coifman and Wickerhauser finds a set of bases that provide the most desirable representation of the data relative to a particular cost function (e.g. entropy).

The implementation part of wavelet packets can be found in MATLAB wavelet toolbox in the link give below http://www.mathworks.com/access/helpdesk/help/toolbox/wavelet/index.html?/access/helpdesk/help/toolbox/wavelet/ch05_use.html

The illustration and implementation of wavelet packets along with its code in C++ is given in the link below http://www.bearcave.com/misl/misl_tech/wavelets/packet/index.html

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