Linear transformation of Gaussian data (ES approach)

This building-block considers the linear reduction of “Gaussian-like" data, corresponding to row “Gaussian" in Table 3.1. By this, we mean sensor data such as raw or averaged acoustic or seismic data that is not constrained to be positive. Approximate Gaussianity is usually a result of naturally-occuring averaging (central-limit theorem) effects. We may also consider spectral or intensity data that is averaged or non-linearly transformed (i.e. the logarithm), or both. An example is the last stage in the calculation of MFCC coefficients (truncated DCT of the log band energies). The ES is formed from the sum of the squares of the input samples. Applications are very wide including principal component analysis and linear filtering. For the J-function, rather than assuming a fixed Gaussian variance, we use the “energy statistic" (ES) approach of Section 3.2.2.