Hi RL,
I managed to find the Freq program, but can not get it to run on Windows 10.
However I did manage to open the help menu and this is how the program works.
"The usual frequency analysis approach is to pre-process your data, apply a Fast Fourier Transform to the series, and plot the power spectrum. Peaks in the FFT spectrum may correspond to interesting frequencies. However, it is difficult for anyone but a signal processing expert to know how much power in the time series is actually accounted for by a given frequency. It is even harder to resolve nearby, overlapping broad peaks. More often than not, "noise" dominates the data and cannot easily be de-coupled from signals of interest.
Pre-processing (filtering and windowing) of data sets is a very demanding discipline, and many of the rules to assure the validity of pre-processing operations are difficult to apply, as such
operations actually modify the characteristics of the manipulated data.
Further, most researchers with a need for waveform analyses do not have formal training in the subject, and many feel uncomfortable with having to use a host of implicit assumptions.
There is an alternative, nearly painless method available to perform such frequency analyses. The researcher first prepares (as a text file) a table of candidate periods. On initial creation, the table usually contains a fairly large number of entries, as there may be no prior knowledge of what is really present in the data. Periods may be longer than the time series, or as short as twice the time interval between points. But the researcher often knows what to look for based on theory or existing work, and the table will contain several periods in the regions of interest.
FREQ is not just a curve-fitter, nor is it simply an FFT. To use it, you should know something about your data, but you need nearly no data analysis background. FREQ searches your data using the supplied candidate periods in a .TBL file which you prepare, selecting those periods which account for the most "power".
FREQ uses an adaptation, called Fast Orthogonal Search (FOS), of the Orthogonal Search Method developed by Michael J. Korenberg and his group at Queens University in the late 1980's. The algorithm is applied to your data set, using an associated table of candidate periods. The precise power, amplitude, and phase of sine waves corresponding to entries in the table is displayed. The objective is to determine if frequencies of interest to the researcher are present in significant measure, and report the results.
The algorithm analyzes a time series stepwise, determining the ability of each period to explain a significant portion of the total variance (mean square error, or MSE: roughly, the data set's "power"). It then orthogonally removes the sinusoid explaining the largest percentage of the time series variance. This process is repeated on the residuals until there is no further significant error reduction or until a specified number of periods have been identified.
The algorithm is capable of much greater time resolution than a Fourier transform, and is not limited to harmonics of a fundamental frequency. It is also quite insensitive to noise, as all data elements are used only in series-wide averages over the orthogonal basis functions. Finally, it tolerates missing data points, irregularly-spaced data sets, and short data segments. In many nonlinear or biological systems, the signal frequencies move, or breathe, as the system evolves, so short segments are necessary for system identification."
Spot9