Method of producing noise free frequency spectrum signals

A spectroscopy method comprising:

• (a) producing an output signal being the output of a spectrometer, said signal comprising the summation of signals of multiple frequencies;
• (b) digitizing and sampling the two components of the output signal which are .pi./2 radians out-of-phase at spaced time intervals to produce time series data;
• (c) converting the time series data to a frequency spectrum by finding frequencies and attentuation constants of wave elements by use of an autoregressive model comprising:
• i) applying a fitting method to the time series data using the frequencies and attenuation constants of the data to find initial amplitudes and phases of n waves by selecting n solutions from the solutions of each order m according to a predetermined method and applying the fitting method thereto;
• ii) calculating Akaike's information criterion, AIC (m, n), from the parameters m and n by successively substituting the values of the n waves according to the method of selection;
• iii) finding a combination for order m.sub.o and the number of solutions n.sub.o which minimize the AIC (m, n);
• iv) selecting substituted n.sub.0 solutions from the solutions of the order m.sub.o ;
• and
• d) displaying the selected solutions as a noise free frequency spectrum.

A spectroscopy method comprising:

• (a) producing an output signal being the output of a spectrometer, said signal comprising the summation of signals of multiple frequencies;
• (b) digitizing and sampling the two components of the output signal which are .pi./2 radians out-of-phase at spaced time intervals to produce time series data;
• (c) converting the time series data to a frequency spectrum by finding frequencies and attenuation constants of wave elements by use of an autoregressive model comprising:
• i) comparing the powers or the initial amplitudes of waves of the same order m of the autoregressive model with respect to the solutions of each order m and sorting the solutions in descending order of powers or the initial amplitudes for the waves of each order m;
• ii) selecting n solutions successively from the solutions of each order m according to the sequencing and applying the least squares method to the time series data using the frequencies and the attenuation constants of n waves of the signal to find the initial amplitudes and the phases of the n waves;
• iii) calculating Akaike's information criterion, AIC (m, n) from the parameters m and n by successively substituting the values of the n waves according to the sequencing;
• iv) finding a combination of order m.sub.o and the number of solutions n.sub.o which minimizes the AIC (m, n);
• v) selecting n.sub.o solutions of upper orders from the solutions of the order m.sub.o according to the sequencing;
• d) displaying the selected solutions as a noise free frequency spectrum.