fourfilt

  FOURFILT  Fourier low, high, or bandpass filter.

     [filtdat]=fourfilt(x,delt,tmax,tmin)

     where:   x:      data series to be filtered
              delt:   sampling interval
              tmax:   maximum period filter cutoff
              tmin:   minimum period filter cutoff

     usage:  lowpassdata=fourfilt(data,0.5,2000,20)

               gives lowpass filter with cutoff at 20.0 sec
               tmax set > (length(x)*delt) for no cutoff at low freq end

     usage:  highpassdata=fourfilt(x,0.5,20,0.9)

               gives highpass filter with cutoff at 20.0 sec
               tmin set < (2*delt) for no cutoff at high freq end

     usage:  bandpassdata=fourfilt(x,0.5,20,10)

               gives bandpass filter passing 10-20 sec. band
 
 Reference:
 Walters, R. A.  and Heston, C., 1982. Removing the tidal-period variations from time-series
 data using low-pass digital filters. Journal of Physical Oeanography, 12 112-115 .

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 Version 1.0  (12/4/96)  Jeff List (jlist@usgs.gov)
 Version 1.1  (1/8/97)  Rich Signell (rsignell@usgs.gov)
     removed argument for number of points and add error trapping for matrices
 Version 1.1b (12/1/2005) Rich Signell (rsignell@usgs.gov)
     added reference
%%%%%%%%%%%%%%%%%%%%%%%%%%%%

0001 function [filtdat]=fourfilt(x,delt,tmax,tmin)
0002 
0003 %  FOURFILT  Fourier low, high, or bandpass filter.
0004 %
0005 %     [filtdat]=fourfilt(x,delt,tmax,tmin)
0006 %
0007 %     where:   x:      data series to be filtered
0008 %              delt:   sampling interval
0009 %              tmax:   maximum period filter cutoff
0010 %              tmin:   minimum period filter cutoff
0011 %
0012 %     usage:  lowpassdata=fourfilt(data,0.5,2000,20)
0013 %
0014 %               gives lowpass filter with cutoff at 20.0 sec
0015 %               tmax set > (length(x)*delt) for no cutoff at low freq end
0016 %
0017 %     usage:  highpassdata=fourfilt(x,0.5,20,0.9)
0018 %
0019 %               gives highpass filter with cutoff at 20.0 sec
0020 %               tmin set < (2*delt) for no cutoff at high freq end
0021 %
0022 %     usage:  bandpassdata=fourfilt(x,0.5,20,10)
0023 %
0024 %               gives bandpass filter passing 10-20 sec. band
0025 %
0026 % Reference:
0027 % Walters, R. A.  and Heston, C., 1982. Removing the tidal-period variations from time-series
0028 % data using low-pass digital filters. Journal of Physical Oeanography, 12 112-115 .
0029 %
0030 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0031 % Version 1.0  (12/4/96)  Jeff List (jlist@usgs.gov)
0032 % Version 1.1  (1/8/97)  Rich Signell (rsignell@usgs.gov)
0033 %     removed argument for number of points and add error trapping for matrices
0034 % Version 1.1b (12/1/2005) Rich Signell (rsignell@usgs.gov)
0035 %     added reference
0036 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0037 [m,n]=size(x);
0038 if(min(m,n)~=1),
0039   disp('fourfilt cannot handle matrices');
0040   stop
0041 end
0042 npts=length(x);
0043 
0044 nby2=npts/2;
0045 tfund=npts*delt;
0046 ffund=1.0/tfund;
0047 
0048 %  remove the mean from data:
0049 
0050 datamean=mean(x);
0051 x=x-datamean;
0052 
0053 % fourier transform data:
0054 
0055 coeffs=fft(x);
0056 
0057 %  filter coefficients:
0058 
0059 f=ffund;
0060 for i=2:nby2+1
0061   t=1.0/f;
0062   if t > tmax | t < tmin
0063      coeffs(i)=0.0*coeffs(i);
0064   end
0065   f=f+ffund;
0066 end
0067 
0068 
0069 %  calculate the remaining coefficients:
0070 
0071 for i=2:nby2
0072    coeffs(npts+2-i)=conj(coeffs(i));
0073 end
0074 
0075 
0076 %  backtransform data and take real part:
0077 
0078 backcoeffs=ifft(coeffs);
0079 filtdat=real(backcoeffs);
0080 
0081 % add back the mean:
0082 
0083 filtdat=filtdat+datamean;