
Here is a little program that filters time series data for emphasis of specific 
signal wavelengths.

Note.  All filtering mothods do not remove all variability on time
	scales e.g., > or < 80 years. If you specify a bandwidth of 80 years, the amplitude
	of a sine wave of wavelength 80 years will be reduced by a half. Longer
	wavelengths will be reduced by less than a half and shorter wavelengths
	by more than a half. It's not a sharp cutoff. The spline fit will be composed of
	longer waves and the residuals of shorter waves.  

User input: <example using fata file Data_low-freq.txt>

 Enter the input file (/ to exit)           ==> Data_low-freq.txt
 Enter the output file                      ==> tst
 Enter number of columns                    ==> 32
 Enter missing value flag e.g., -999.00     ==> -999.0

 Enter the 50% frequency response cutoff    ==> 80



Notes:  

    Percent of variance of spline with
    50.00% of variance at  wavelength of   20.00 years
    so more amplitude > the 50% cutoff will be preserved.
      Wavelength__Variance     Wavelength__Variance     Wavelength__Variance
          6.34      99.0%         15.19      75.0%         28.29      20.0%
          8.01      97.5%         16.81      66.7%         34.64      10.0%
          9.59      95.0%         20.00      50.0%         41.76       5.0%
         11.54      90.0%         23.79      33.3%         49.98       2.5%
         14.14      80.0%         26.32      25.0%         63.09       1.0%


    Percent of variance of spline with
    50.00% of variance at  wavelength of   80.00 years
    so more amplitude > the 50% cutoff will be preserved.
      Wavelength__Variance     Wavelength__Variance     Wavelength__Variance
         25.35      99.0%         60.77      75.0%        113.14      20.0%
         32.05      97.5%         67.26      66.7%        138.55      10.0%
         38.35      95.0%         80.00      50.0%        167.04       5.0%
         46.16      90.0%         95.14      33.3%        199.92       2.5%
         56.55      80.0%        105.28      25.0%        252.35       1.0%

The residual series isjusttheoppositeofthespline,i.e.thesplineissubtracted
fromtheoriginalseriestogettheresiduals.  


This program uses a cubic smoothing spline to filter a time series.  The advantage of using a 
spline, as compared to a FFT proceedure, is there is no loss of end member information.
The ends are interpolated and beyond their real endpoints in order to use the whole series.

NOTE*** You MUST put the attached folder Absoft80 in the top level of your C:drive  you can run this 
program on your computer.  This is important!!!!

The output file looks like this:

 Input series is: Conroy              
 year  unfilt  spline  resids
   41   0.795   0.925  -0.130
   42   0.818   0.939  -0.121
   43   0.841   0.953  -0.112
   44   0.864   0.968  -0.104
   45   0.888   0.984  -0.096

and so on.... for every reconstruction in file: Data_low-freq.txt  what you want is the
spline column:

Finally,
  Note the format of the input data files.  Tab delimited text with no spaces in column
  names.  
  
  Sincerely,
  pjk
  