### Reference Hypothesis

For maximum entropy property, the module designer must choose a reference hypothesis and energy statistic according to the requirements of Section 3.2.2. Since is positive valued, energy statistics may be formed by any weighted (with positive weights) sum of the samples of

 (5.3)

where . This class of energy statistic then has the properties of a norm (See section 3.2.2) The canonical reference hypothesis corresponding to this energy statistic is then

Note that there is no reason to use another reference hypothesis since all reference hypotheses that depend on the data only through feature will produce the same resultant projected PDF [5]. The only difference lies in the tractability of and for this class, we provide a solution.

If the matrix A is already pre-defined, one must determine an energy statistic that is contained in (i.e. determine the weights in (5.3). For example, if matrix implements the DCT, then the first column is just a constant. This suggests the energy statistic

When in doubt and if matrix can be modified, it may be reasonable to seek the energy statistic that computes the total energy of the source. Since generally comes from the magnitude-squared output bins of an orthogonal transform, such as FFT, it may be useful to use the energy statistic

which computes the total energy of the source (input of the orthogonal transform). A special case of this is if matrix implements the auto-correlation function (ACF), then the statistic

is suggested (see Section 5.2.2).

Baggenstoss 2017-05-19