Spectral Line Measurements in Exceptionally Low SNR Achieved by Virtue of the KLT (Karhunen-Loeve Transform)

摘要

A little-known tool for spectral line measurements is the KLT (Karhunen-Loeve Transform). This mathematical algorithm is superior to the classical FFT in that: 1) The KLT can filter signals out of the background noise over both wide and narrow bands. On the contrary, the FFT rigorously applies to narrow-band signals only. 2) The KLT can be applied to random functions that are non-stationary in time, i.e. whose autocorrelation is a function of the two independent variables t_1 and t_2 separately. Again, this is a sheer advantage of the KLT over the FFT, since the FFT rigorously applies to stationary processes only, i.e. when the autocorrelation is a function of the absolute value of the difference of t_1 and t_2. 3) The KLT can detect signals embedded in noise to unbelievably small values of the Signal-to-Noise Ratio (SNR), like 10~(-3) or so. This particular feature of the KLT is described in detail in this paper.