Wavelet packet decomposition

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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.

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, where we want as many small values as possible, the standard wavelet transform may not produce the best result, since it is limited to wavelet bases that increase by a power of two with each step. It could be that another combination of bases produce a more desirable representation. The best basis algorithm finds a set of wavelet bases (which filters among the set of possible filters to use) that provide the most desirable representation of the data relative to a particular cost function.