Feature transformation and Energy Statistic

where is a non-singular matrix. Because the data is positive, a positive-weighted sum of the input data meets the conditions of a norm on , which is the positive quadrant of . We apply row ``Exponential" in Table 3.1. The ES is the sum of the input samples, which is also a linear transformation, and so can be integrated into matrix . In order that contain the ES, we need that

where .

An example of this is MEL frequency band analysis, covered in Section 5.2.6, where the columns of are the MEL band functions. The sum of the standard MEL band functions is a constant, if the zero and Nyquist frequency bands are present, meeting requirement (5.2). Another example is in auto-regressive spectral analysis [25] where matrix computes the auto-correlation function (ACF), covered in Section 5.2.2, where the zero-th lag ACF coefficient is defined in Table 3.1.

Baggenstoss 2017-05-19