Spectral Line Measurements in Exceptionally Low SNR by the KLT
- Paper number
IAC-07-A4.1.03
- Author
Dr. Francesco Schillirò, National Institute for Astrophysics, Italy
- Coauthor
Mr. Salvatore Pluchino, Visiting Research Fellow, IRA-INAF Radiotelescopes, Italy
- Coauthor
Dr. Claudio Maccone, Member of the International Academy of Astronautics, Italy
- Year
2007
- Abstract
A little-known tool for spectral line measurements is the KLT (acronym for Karhunen-Loève Transform). This mathematical algorithm is superior to the classical FFT in many regards:1) The KLT can filter signals out of the background noise over both wide and narrow bands. That is in sharp contrast to the FFT that 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 t1 and t2 separately. Again, this is a sheer advantage of the KLT over the FFT, inasmuch as the FFT rigorously applies to stationary processes only, i.e. processes whose autocorrelation is a function of the absolute value of the difference of t1 and t2 only.3) It can detect signals embedded in noise to unbelievably small values of the Signal-to-Noise Ratio (SNR), like 10e-4 or so. This particular feature of the KLT is studied in detail in this paper. As a practical application, we show the case of a 43 GHz line emission produced by SiO and detected experimentally in R Cassiopeae by virtue of the KLT already available at the IRA-INAF Noto radiotelescope in Sicily, Italy.
- Abstract document