pl64

 low pass filter (33 hr) 
 PL66TN: pl66t for variable dt and T
 xf=PL66TN(x,dt,T) computes low-passed series xf from x
 using pl66 filter, with optional sample interval dt (hrs)
 and filter half amplitude period T (hrs) as input for
 non-hourly series.

 INPUT:  x=time series (must be column array)
         dt=sample interval time [hrs] (Default dt=1)
         T=filter half-amp period [hrs] (Default T=33)

 OUTPUT: xf=filtered series

0001 function xf=pl66tn(x,dt,T);
0002 % low pass filter (33 hr)
0003 % PL66TN: pl66t for variable dt and T
0004 % xf=PL66TN(x,dt,T) computes low-passed series xf from x
0005 % using pl66 filter, with optional sample interval dt (hrs)
0006 % and filter half amplitude period T (hrs) as input for
0007 % non-hourly series.
0008 %
0009 % INPUT:  x=time series (must be column array)
0010 %         dt=sample interval time [hrs] (Default dt=1)
0011 %         T=filter half-amp period [hrs] (Default T=33)
0012 %
0013 % OUTPUT: xf=filtered series
0014 
0015 % NOTE: both pl64 and pl66 have the same 33 hr filter
0016 % half-amplitude period. pl66 includes additional filter weights
0017 % upto and including the fourth zero crossing at 2*T hrs.
0018 
0019 % The PL64 filter is described on p. 21, Rosenfeld (1983), WHOI
0020 % Technical Report 85-35. Filter half amplitude period = 33 hrs.,
0021 % half power period = 38 hrs. The time series x is folded over
0022 % and cosine tapered at each end to return a filtered time series
0023 % xf of the same length. Assumes length of x greater than 132.
0024 
0025 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0026 % 10/30/00
0027 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0028 
0029 % default to pl64
0030 if (nargin==1); dt=1; T=33; end
0031 
0032 cutoff=T/dt;
0033 fq=1./cutoff;
0034 nw=2*T./dt;
0035 nw=round(nw);
0036 %disp(['number of weights = ',int2str(nw)])
0037 nw2=2.*nw;
0038 
0039 [npts,ncol]=size(x);
0040 if (npts<ncol);x=x';[npts,ncol]=size(x);end
0041 xf=x;
0042 
0043 % generate filter weights
0044 j=1:nw;
0045 t=pi.*j;
0046 den=fq.*fq.*t.^3;
0047 wts=(2.*sin(2.*fq.*t)-sin(fq.*t)-sin(3.*fq.*t))./den;
0048 % make symmetric filter weights
0049 wts=[wts(nw:-1:1),2.*fq,wts];
0050 wts=wts./sum(wts);% normalize to exactly one
0051 % plot(wts);grid;
0052 % title(['pl64t filter weights for dt = ',num2str(dt),' and T = ',num2str(T)])
0053 % xlabel(['number of weights = ',int2str(nw)]);pause;
0054 
0055 % fold tapered time series on each end
0056 cs=cos(t'./nw2);
0057 jm=[nw:-1:1];
0058 
0059 for ic=1:ncol
0060 % ['column #',num2str(ic)]
0061  jgd=find(~isnan(x(:,ic)));
0062  npts=length(jgd);
0063  if (npts>nw2)
0064 %detrend time series, then add trend back after filtering
0065   xdt=detrend(x(jgd,ic));
0066   trnd=x(jgd,ic)-xdt;
0067   y=[cs(jm).*xdt(jm);xdt;cs(j).*xdt(npts+1-j)];
0068 % filter
0069   yf=filter(wts,1.0,y);
0070 % strip off extra points
0071   xf(jgd,ic)=yf(nw2+1:npts+nw2);
0072 % add back trend
0073   xf(jgd,ic)=xf(jgd,ic)+trnd;
0074  else
0075  'warning time series is too short'
0076  end
0077 end