Wavelet packet functions

What do wavelet packet functions look like ... 

Before we answer the question addressing this section, we probably need to take a brief look at wavelet packet functions from the continuous side. 

For each column in data matrix, select wavelet packet function and wavelet... 

Basically, in WPD, for fixed values of / and fe, analyses the fluctuations of the signal roughly around the position 2 fe, at scale 2 and oscillation parameter n. WPA operates by approximating a signal with scaled and translated wavelet packet functions,... 

It should be emphasised that Equation 4.35 allows many possible combinations of wavelet packet functions to be... 

Several extensions of wavelets have been developed to improve their ability to solve practical problems. Wavelet packets (Coifman and Wick-erhauser, 1992) are a library of basis functions that cover a wide variety of shapes. The library can be searched efficiently to select the best set of... 

Unlike representation of functions using wavelet basis functions, there are many different combinations of wavelet packet basis functions that can be used in signal representation. Hence there is some degree of redundancy. With redundancy comes choice, and Section 3 discusses one approach for selecting a set of basis functions. 

The best basis algorithm seeks a basis in the WPT which optimizes some criterion function. Thus, the best basis algorithm is a task-specific algorithm in that the particular basis is dependent upon the role for which it will be used. For example, a basis chosen for compressing data may be quite different from a basis that might be used for classifying or calibrating data, since different criterion functions would be optimized. The wavelet packet coefficients which are resultant of the best basis, may then be used for some specific task such as compression or classification for instance. 

One commonly used cost function particularly in data compression is entropy. If we let Wj t j denote the ith wavelet packet coefficient band(j, t) of the wavelet packet transform, then the entropy-like criterion for band(j, t) is defined as follows ... 

Perform the wavelet packet transform using filter coefficients associated with the Haar wavelet and scaling functions, then, compute the wavelet packet coefficients associated with the best basis using the entropy cost function for the signal x = (0.0000,0.0491.0.1951,0.4276,0.7071,0.9415,0.9808,0.6716). 

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