Feature PDF (Spectral Histogram)

For a small number of sinusiods, the total number of parameters for the SINAR model is small, so the feature PDF can be approximated by Gaussian mixtures, etc. The function software/module_sinar_test.m implements the acid using Gaussian mixtures test with method='gmm'. However, for more sinusoids, a PDF estimation method more suited for SINAR should be used. The fixed parameters for the SINAR model of AR order and sinusoids include the AR parameter estimates , , the vector of frequencies , and the -dimensional vector of real and imaginary amplitudes . Let be an arbitrary (real data) hypothesis and assume we want to estimate . We make the simplifying assumption that the AR and sinusoidal parameters are independent:

If we expand

we can implement as a histogram. If we assume the individual frequencies are independent, we have

where is the frequency histogram for class . In addition, we can assume a standard exponential distribution for the squared magnitudes,

where can be constant or can depend on the frequency. In the second case, a means of estimating should be used. These ideas are implemented by the function software/spect_hist.m. The function software/module_sinar_test.m implements the acid using histogram with method='hist'.

Baggenstoss 2017-05-19