SegmentedSmooth.m

function SmoothedSignal=SegmentedSmooth(y,smoothwidths,type,ends)
% SegmentedSmooth(y,w,type,ends) divides y into a number of equal-length
% segments defined by the length of the vector 'smoothwidths', then
% smooths each segment with smooth of type 'type' and width defined by
% the elements of vector 'smoothwidths'. Same syntax as fastsmooth.
% Version 1, November 2016.
% The argument "type" determines the smooth type:
%    If type=1, rectangular (sliding-average or boxcar) 
%    If type=2, triangular (2 passes of sliding-average)
%    If type=3, pseudo-Gaussian (3 passes of sliding-average)
%    If type=4, pseudo-Gaussian (4 passes of same sliding-average)
%    If type=5, multiple-width (4 passes of different sliding-averages)
% The argument "ends" controls how the "ends" of the signal 
%   (the first w/2 points and the last w/2 points) are handled.
%    If ends=0, the ends are zero. (In this mode the elapsed 
%       time is the fastest and is independent of the smooth width).
%    If ends=1, the ends are smoothed with progressively 
%       smaller smooths the closer to the end. (In this mode the  
%       elapsed time increases with increasing smooth widths).
% SegmentedSmooth(Y,w,type) smooths with ends=0.
% SegmentedSmooth(Y,w) smooths with type=1 and ends=0.
%
% Examples: 3-segment smooth of random white noise, smooth widths of
%   2,20, and 200.
%     x=1:10000;y=randn(size(x));
%     plot(x,SegmentedSmooth(y,[2 20 200],3,0))
%
%     20-segment smooth, odd smooth widths from 1 to 41:
%     plot(x,SegmentedSmooth(y,[1:2:41],3,0))
 
%   Copyright (c) 2012, Thomas C. O'Haver
%   
%   Permission is hereby granted, free of charge, to any person obtaining a copy
%   of this software and associated documentation files (the "Software"), to deal
%   in the Software without restriction, including without limitation the rights
%   to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
%   copies of the Software, and to permit persons to whom the Software is
%   furnished to do so, subject to the following conditions:
%   
%   The above copyright notice and this permission notice shall be included in
%   all copies or substantial portions of the Software.
%   
%   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
%   IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
%   FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
%   AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
%   LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
%   OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
%   THE SOFTWARE.

if nargin==2, ends=0; type=1; end
if nargin==3, ends=0; end
ly=length(y);
NumSegments=length(smoothwidths);
SegLength=round(ly./NumSegments);
SmoothSegment=zeros(ly,NumSegments);
SmoothedSignal=zeros(1,ly);
for Segment=1:NumSegments,
    SmoothSegment(:,Segment)=fastsmooth(y,smoothwidths(Segment),type,ends);
    startindex=(1+(Segment-1)*SegLength);
    endindix=startindex+SegLength-1;
    if endindix>ly,endindix=ly;end
    indexrange=startindex:endindix;
    SmoothedSignal(indexrange)=SmoothSegment(indexrange,Segment);
end

function SmoothY=fastsmooth(Y,w,type,ends)
% fastsmooth(Y,w,type,ends) smooths vector Y with smooth 
%  of width w. Version 3.0, October 2016.
% The argument "type" determines the smooth type:
%   If type=1, rectangular (sliding-average or boxcar) 
%   If type=2, triangular (2 passes of sliding-average)
%   If type=3, pseudo-Gaussian (3 passes of sliding-average)
%   If type=4, pseudo-Gaussian (4 passes of same sliding-average)
%   If type=5, multiple-width (4 passes of different sliding-average)
% The argument "ends" controls how the "ends" of the signal 
% (the first w/2 points and the last w/2 points) are handled.
%   If ends=0, the ends are zero.  (In this mode the elapsed 
%     time is independent of the smooth width). The fastest.
%   If ends=1, the ends are smoothed with progressively 
%     smaller smooths the closer to the end. (In this mode the  
%     elapsed time increases with increasing smooth widths).
% fastsmooth(Y,w,type) smooths with ends=0.
% fastsmooth(Y,w) smooths with type=1 and ends=0.
% Examples:
% fastsmooth([1 1 1 10 10 10 1 1 1 1],3)= [0 1 4 7 10 7 4 1 1 0]
%
% fastsmooth([1 1 1 10 10 10 1 1 1 1],3,1,1)= [1 1 4 7 10 7 4 1 1 1]
%
% x=1:100;
% y=randn(size(x)); 
% plot(x,y,x,fastsmooth(y,5,3,1),'r')
% xlabel('Blue: white noise.    Red: smoothed white noise.')
%
% Copyright (c) 2012, Thomas C. O'Haver
% 

  switch type
    case 1
       SmoothY=sa(Y,w,ends);
    case 2   
       SmoothY=sa(sa(Y,w,ends),w,ends);
    case 3
       SmoothY=sa(sa(sa(Y,w,ends),w,ends),w,ends);
    case 4
       SmoothY=sa(sa(sa(sa(Y,w,ends),w,ends),w,ends),w,ends);
    case 5
       SmoothY=sa(sa(sa(sa(Y,round(1.6*w),ends),round(1.4*w),ends),round(1.2*w),ends),w,ends);
  end

function SmoothY=sa(Y,smoothwidth,ends)
w=round(smoothwidth);
SumPoints=sum(Y(1:w));
s=zeros(size(Y));
halfw=round(w/2);
L=length(Y);
for k=1:L-w,
   s(k+halfw-1)=SumPoints;
   SumPoints=SumPoints-Y(k);
   SumPoints=SumPoints+Y(k+w);
end
s(k+halfw)=sum(Y(L-w+1:L));
SmoothY=s./w;
% Taper the ends of the signal if ends=1.
  if ends==1,
  startpoint=(smoothwidth + 1)/2;
  SmoothY(1)=(Y(1)+Y(2))./2;
  for k=2:startpoint,
     SmoothY(k)=mean(Y(1:(2*k-1)));
     SmoothY(L-k+1)=mean(Y(L-2*k+2:L));
  end
  SmoothY(L)=(Y(L)+Y(L-1))./2;
  end