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GCPeakDetection.m
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GCPeakDetection.m
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function resPeaks = GCPeakDetection(gcData, timesteps, splitSignalSize, ...
degPoly, thresholdSD, thresholdFD, thresholdSignal, splitCoeultion, ...
showPlot, maxYLimPlot)
%
% function to find 1D Chromatogram peaks using Savitzky-Golay smoothing.
%
% INPUTS:
% -- gcData : a vector containing the values of GC measurements
% -- timesteps : a vector of equal length to gcData, containing the elution
% times of the recording. If this input is not given or is empty, then
% the default is time index.
% -- splitSignalSize : 0 if not splitting the input signal into smaller
% chunks for peak detection, default is 100 (input is empty).
% -- degPoly : the degree of polynomial for the SG smoothing, default is 3.
% -- thresholdSD : threshold for the second derivative, any SD below this
% threshold is considered a candidate for peak. The input should be in
% a vector of two values: [v1, v2], where v1 indicates
% whether it's a absolute value threshold (1) or a relative value to
% the noise (0), v2 is a value for the actual threshold. Default is [0
% 5], i.e. 5 times the noise.
% -- thresholdFD : threshold for the first derivative, where we consider
% the start and end of any peak. The input is in the same format as
% thresholdSD. Default is [0 2]. Note, [1 0.05] seems to be
% reasonable for normalised data.
% -- thresholdSignal : threshold above which the data is considered a
% signal and not some impurity or noise. The input is in the same
% format as thresholdSD, except if v1 = 0, then threshold is
% (baseline + v2 * noise). Default is [0 2].
% -- splitCoeultion : true if want to split the strong co-elution peaks,
% use with caution. default if false
% -- showPlot : true if want to see the peak detection in action. default
% is false.
% -- maxYLimPlot : value for the maximum y-axis for the plot. default is
% min(1000, max(gcData))
%
% OUTPUTS:
% -- resPeaks : a mx5 matrix of m peaks found in the input data, each row
% is in the order of [peak start; peak end; peak maximum; peak height;
% peak area], the first 3 values are either time index or elution time
% depending on whether the second input is given or not.
%
% Written according to the paper: Vivo-Truyols et al. "Automatic program
% for peak detection and deconvolution of multi-overlapped chromatographic
% signals, Part I: Peak detection", Journal of Chromatography A, vol. 1096
% (2005) pp 133-145
%
% Released under GNU General Public Licence v3.
%
% X. Rosalind Wang
% CSIRO
% September 2013
%--
% Initialisation, checking input data, and setting default values
%--
if size(gcData, 1) > 1 && size(gcData, 2) > 1
error('data input should be a 1D vector.');
end
N = length(gcData);
if nargin < 2 || isempty(timesteps)
timesteps = 1 : N;
end
if size(timesteps, 1) > 1 && size(timesteps, 2) > 1
error('time step input should be a 1D vector.');
elseif length(timesteps) ~= N
error('input data and time steps do not match in size.');
end
if nargin < 3 || isempty(splitSignalSize)
splitSignalSize = 100;
end
if splitSignalSize > N
splitSignalSize = 0; % use the whole signal
end
if nargin < 4 || isempty(degPoly)
degPoly = 3;
end
if nargin < 5 || isempty(thresholdSD)
% default is 5 * noise of SD
thresholdSD = [0 5];
elseif length(thresholdSD) == 2
% check to make sure the input threshold values are valid
if ~(thresholdSD(1) ~= 0 || thresholdSD(1) ~= 1)
error('Threshold for second derivative input 1 should be 0 or 1');
end
else
error('Threshold for second derivative not valid format');
end
if nargin < 6 || isempty(thresholdFD)
% default is 2 * noise of FD
thresholdFD = [0 2];
elseif length(thresholdFD) == 2
% check to make sure the input threshold values are valid
if ~(thresholdFD(1) ~= 0 || thresholdFD(1) ~= 1)
error('Threshold for first derivative first input should be 0 or 1');
end
else
error('Threshold for first derivative not valid format');
end
if nargin < 7 || isempty(thresholdSignal)
% default is baseline + 2 * noise
thresholdSignal = [0 2];
elseif length(thresholdSignal) == 2
% check to make sure the input threshold values are valid
if ~(thresholdSignal(1) ~= 0 || thresholdSignal(1) ~= 1)
error('Threshold for signal input 1 should be 0 or 1');
end
else
error('Threshold for signal not valid format');
end
if nargin < 8 || isempty(splitCoeultion)
splitCoeultion = false;
end
if nargin < 9
showPlot = false;
end
if showPlot && nargin < 10
if max(gcData) > 1000
yULim = 1000;
else
yULim = max(gcData);
end
elseif ~showPlot && nargin < 10
yULim = max(gcData);
else
yULim = maxYLimPlot;
end
% initialise the output matrix
resPeaks = zeros(0, 5);
colPeakStart = 1;
colPeakEnd = 2;
colPeakMax = 3;
colPeakHeight = 4;
colPeakArea = 5;
if showPlot
props = {'LineWidth', 1};
hFig = figure(1);
clf;
plot(timesteps, gcData, props{:});
set(gca, 'YLim', [0 yULim]);
grid on;
hold on;
end
%==================
% STEP 1 : Dividing the input signal into managable chunks
% -- run an initial SG smoothing to find signal's noise
% -- divide the signal into roughly size of splitSignalSize, but making
% sure that no actual signal is divided up.
% initial smooth, using window size 5.
smdInitial = sgolayfilt(gcData, degPoly, 5, 0);
% calculate the noise
% turns out using the noise criterion defined in the calcNoise function
% below doesn't work well here, so just going to use the median value
noiseSmdInitial = calcNoise(smdInitial);
baselineSmdInitial = median(smdInitial);
if ~thresholdSignal(1)
thrSig = baselineSmdInitial + thresholdSignal(2) * noiseSmdInitial;
else
thrSig = thresholdSignal(2);
end
% find all indices where the smoothed signal is less than noise x 2
% indNoiseSmdInitial = find(smdInitial < thrSig);
% plot the threshold for noise
if showPlot
figure(hFig);
plot(timesteps, smdInitial, 'r:', props{:});
plot([timesteps(1), timesteps(end)], [thrSig, thrSig], ...
'b--', 'LineWidth', 1);
end
% find all the partitions, save the start of the partition indices
if splitSignalSize == 0
% TODO: make sure this bit makes sense.
partStIndex = 1;
partEndIndex = N;
else
[partStIndex, partEndIndex] = partitionSignal(smdInitial, ...
thrSig, N, splitSignalSize);
end
% total number of partitions
NPartition = length(partStIndex);
% plot these partitions out
if showPlot
figure(hFig);
for i = 1 : length(partStIndex)
plot([timesteps(partStIndex(i)) timesteps(partStIndex(i))], [0 yULim], 'k--');
end
end
% if the total number of partition found is too small, i.e. the signal
% threshold was set too low, then we need to reset that.
% nb. this isn't in the referneced paper either.
if splitSignalSize && NPartition <= 3
% if the threshold was set to a certain value, then use noise as the
% threshold, if we used noise as a threshold, then double the threshold
% value
if thresholdSignal(1) == 1
thresholdSignal = [0 2];
elseif thresholdSignal(1) == 0
thresholdSignal(2) = thresholdSignal(2) * 2;
else
% we shouldn't get in here, but let's be safe
error('Threshold for signal input 1 should be 0 or 1');
end
thrSig = baselineSmdInitial + thresholdSignal(2) * noiseSmdInitial;
% recalculate the partitions
[partStIndex, partEndIndex] = partitionSignal(smdInitial, ...
thrSig, N, splitSignalSize);
NPartition = length(partStIndex);
% replot if the flag was on
if showPlot
figure(hFig);
for i = 1 : length(partStIndex)
plot([timesteps(partStIndex(i)) timesteps(partStIndex(i))], ...
[0 yULim], 'k--');
end
end
end
if showPlot
fprintf('Chromatogram split into smaller sections. \n');
fprintf('Press any key to continue... \n\n');
pause;
end
%==================
% Find peaks for each partition of the data
NPeaksTotal = 0;
for partNumb = 1 : NPartition
% get the data associated with this section
dataPartOrig = gcData( partStIndex(partNumb) : partEndIndex(partNumb) );
smdInitPart = smdInitial( partStIndex(partNumb) : partEndIndex(partNumb) );
NDataPart = length(dataPartOrig);
timePart = timesteps( partStIndex(partNumb) : partEndIndex(partNumb) );
% If any signal in this partition is larger than the threshold for
% signal we defined earlier, then we'll check for peaks
if any(smdInitPart - thrSig > 0)
%==================
% STEP 2: find the best window size for the smoothing
% -- search through all odd size between 5 and 41
% -- use the Durbin-Watson (DW) test
% -- best ws is one which give DW closest to 2
maxWinSize = 41;
if partNumb == NPartition && length(dataPartOrig) < maxWinSize+4
maxWinSize = length(dataPartOrig) - 5;
end
windowSize = 5 : 2 : maxWinSize;
valDW = zeros(length(windowSize), 1);
for wsi = 1 : length(windowSize)
dataPartSmd = sgolayfilt(dataPartOrig, degPoly, windowSize(wsi), 0);
diffSmdOrig = dataPartOrig - dataPartSmd;
valDW(wsi) = ...
sum( ( diffSmdOrig(2:end) - diffSmdOrig(1:end-1) ) .^2 ) ./ ...
sum( diffSmdOrig .^2 ) * ( NDataPart / (NDataPart-1) );
end
% find the difference between the DW values and 2
diffDWn2 = abs(valDW - 2);
% find the actual window size
[temp, indWS] = min(diffDWn2); %#ok<ASGLU>
WS = windowSize(indWS);
% fprintf('window size: %d\n', WS);
% the smoothed data using the discovered window size
% ZD - zero-th derivative
smdZD = sgolayfilt(dataPartOrig, degPoly, WS, 0);
if showPlot
propsPart = {'LineWidth', 2};
hFigPart = figure(2);
clf;
title(sprintf('Partition Number %d', partNumb), 'FontSize', 14);
hold on
plot(timePart, dataPartOrig, 'b-', propsPart{:});
plot(timePart, smdZD, 'r:', propsPart{:});
if max(dataPartOrig) > yULim
set(gca, 'YLim', [0 yULim]);
end
grid on
end
%==================
% STEP 3 : Peak Detection
% We'll only do the peak detection if the signal in the partition is
% more than the threshold set
%---- comment out the previous "if any( > 0)" line and uncomment
%the following if you want to see what the signal in the partition
%looks like
%if any(smdZD - thrSig > 0)
%==================
% STEP 3a. calculate derivatives
% first derivative
smdFD = sgolayfilt(dataPartOrig, degPoly, WS, 1);
% second derivative
smdSD = sgolayfilt(dataPartOrig, degPoly, WS, 2);
% third derivative -- only to be used for moderate co-elutions
smdTD = sgolayfilt(dataPartOrig, degPoly, WS, 3);
% plot first and second derivative
if showPlot
figure(hFigPart);
plot(timePart, smdFD, 'g--', propsPart{:});
plot(timePart, smdSD, 'm-.', propsPart{:});
legend('original data', 'SG smoothed', 'SG 1st derivative', ...
'SG 2nd derivative');
end
%==================
% STEP 3b. use noise of the SD to threshold the zones of -ve SD
% calculate noise
noiseSD = calcNoise(smdSD);
% threshold is either some multiple of the noise, or a set value
if ~thresholdSD(1)
thrSD = thresholdSD(2) * noiseSD;
else
thrSD = thresholdSD(2);
end
% plot the threshold for SD and the signal
if showPlot
figure(hFigPart);
plot([timePart(1), timePart(end)], [-thrSD, -thrSD], ...
'b--', 'LineWidth', 1);
plot([timePart(1), timePart(end)], [thrSig, thrSig], ...
'--', 'LineWidth', 1, 'Color', [0.33 0 0]); % dark red
end
%==================
% STEP 3c. find the negative zones of second derivative
% find SD less than -thrSD
indSD = find(smdSD < -thrSD);
% check if there are any -ve zones
if ~isempty(indSD)
% find, within these indices, the zones of -ve SD, i.e. those with
% continues indices
indIndSD_NegZoneEnd = [find(diff(indSD) > 1), length(indSD)];
indIndSD_NegZoneSta = [1, indIndSD_NegZoneEnd(1:end-1)+1];
% get the actual indices of these zones
indSD_NegZoneEnd = indSD(indIndSD_NegZoneEnd);
indSD_NegZoneSta = indSD(indIndSD_NegZoneSta);
% number of negative zones found
nSDNegZones = length(indSD_NegZoneEnd);
else
nSDNegZones = 0;
end
%==================
% STEP 3d. use the negative zones of SD to find the peaks
% don't think this is necessary.
% % recalculate the signal threshold for this partition
% noiseSmd = calcNoise(smdZD);
% baselineSmd = median(smdZD);
% if ~thresholdSignal(1)
% thrSig2 = baselineSmd + thresholdSignal(2) * noiseSmd;
% else
% thrSig2 = thresholdSignal(2);
% end
% need a threshold for the first derivative for start and end of
% peak
noiseFD = calcNoise(smdFD);
if ~thresholdFD(1)
thrFD = thresholdFD(2) * noiseFD;
else
thrFD = thresholdFD(2);
end
% check to make sure this threshold isn't too big
% don't think this is wise -- only applicable to cases where the
% data is normalised.
% if thrFD > 0.05
% thrFD = 0.05;
% end
% plot FD threshold
if showPlot
figure(hFigPart);
plot([timePart(1), timePart(end)], [thrFD, thrFD], ...
'--', 'LineWidth', 1, 'Color', [0 0.33 0]); % dark green
plot([timePart(1), timePart(end)], [-thrFD, -thrFD], ...
'--', 'LineWidth', 1, 'Color', [0 0.33 0]); % dark green
end
% need change of sign in FD, for checking end of the peak
% -- this isn't in the ref'd paper.
changeInSignFD = abs(diff(smdFD > 0));
% initialise peak results
numbPeaksPart = 0; % number of peaks found in this partition
resPeaksPart = zeros(0, 5);
for nZone = 1 : nSDNegZones
% % first check that the ZD value with the minimum SD is actually
% % above the threshold set for a valid signal
% [temp, indMinSD] = min( ...
% smdSD(indSD_NegZoneSta(nZone):indSD_NegZoneEnd(nZone)) ); %#ok<ASGLU>
% indPeakMax = indSD_NegZoneSta(nZone)+indMinSD-1;
% get the ZD values within the negative zone
smdZDinNegZone = smdZD(indSD_NegZoneSta(nZone):indSD_NegZoneEnd(nZone));
% the peak is the maximum ZD value
[temp, indMaxZD] = max(smdZDinNegZone); %#ok<ASGLU>
indPeakMax = indSD_NegZoneSta(nZone)+indMaxZD-1;
% also check the first derivative in this zone is above the
% threshold for FD -- this bit is not in the ref. paper
smdFDinNegZone = smdFD(indSD_NegZoneSta(nZone):indSD_NegZoneEnd(nZone));
% check to make sure that the previous peak doesn't end after
% the current peak maximum. if so, then we need to do something
% about it in the peak detection loop.
% -- this isn't in the ref'd paper.
prevPeakEndB4CurrPeak = false;
if numbPeaksPart == 0
prevPeakEndB4CurrPeak = true;
elseif timePart(indPeakMax) > resPeaksPart(numbPeaksPart, colPeakEnd)
prevPeakEndB4CurrPeak = true;
end
% conditions for considering this zone:
% -- the smoothed signal in this zone above thrZD, and
% -- any abolute value of FD in this zone is above thrFD.
% else go to the next zone
% -- if the length of the zone is greater than one (not in
% ref'd paper)
if (any(smdZDinNegZone > thrSig)) && (any(abs(smdFDinNegZone) > thrFD)) ...
&& (length(smdZDinNegZone) > 1)
% increment the count of peak numbers in this partition
numbPeaksPart = numbPeaksPart + 1;
% we can write down the time index for the peak maximum and
% its value
resPeaksPart(numbPeaksPart, colPeakMax) = timePart(indPeakMax);
resPeaksPart(numbPeaksPart, colPeakHeight) = smdZD(indPeakMax);
% if previous peak's end is after the current peak maximum,
% then we need to change the peak ending time for the
% previous peak
if ~prevPeakEndB4CurrPeak
% get the index for the end of the previous negative SD
% zone.
indEndPrevSD = indSD_NegZoneEnd(nZone-1);
% starting from this index, we search in the third
% derivative for the change in sign between two time
% indices.
indTemp = indEndPrevSD;
while true
if indTemp > indSD_NegZoneSta(nZone)
indEndPrevSD = indTemp - 1;
break;
elseif diff(smdTD(indTemp:indTemp+1) > 0) == 0
indTemp = indTemp+1;
else
indEndPrevSD = indTemp+1;
break;
end
end
resPeaksPart(numbPeaksPart-1, colPeakEnd) = ...
timePart(indEndPrevSD);
end
% search in the first derivative for start of peak
indFD_startOfPeak = indSD_NegZoneSta(nZone);
while true
% if the current value is at the very first index of
% the partition, then we've found peak
if indFD_startOfPeak == 1
break;
end
% if the current value and the previous value have
% different signs, then we've found start of peak
if changeInSignFD(indFD_startOfPeak-1)
break;
end
% use absolute value of the FD, for those cases where
% the FD at the beginning of the zone isn't positive
if abs(smdFD(indFD_startOfPeak)) > thrFD
% go to the previous FD value
indFD_startOfPeak = indFD_startOfPeak - 1;
else
% found the start of the peak
break;
end
% also check that the previous value is:
% -- the very first value of the partition, or
% -- the same as the last peak's end.
% if so, start found.
if indFD_startOfPeak == 1
break;
elseif numbPeaksPart>1 && ...
timePart(indFD_startOfPeak) == resPeaksPart(numbPeaksPart-1, colPeakEnd)
break;
end
end
% write down the start of the peak
resPeaksPart(numbPeaksPart, colPeakStart) = ...
timePart(indFD_startOfPeak);
% search in the first derivative for the end of the peak
indFD_endOfPeak = indSD_NegZoneEnd(nZone);
while true
% also check that the current value is not the very
% last value of the partition, if so, end found.
if indFD_endOfPeak == NDataPart
break;
end
% if the current value and the next value have
% different signs, then we've found peak end
if changeInSignFD(indFD_endOfPeak)
break;
end
% absolute value of the FD above the threshold, for
% those cases that the FD at the end of the zone isn't
% negative.
if abs(smdFD(indFD_endOfPeak)) > thrFD
% go to the next FD value
indFD_endOfPeak = indFD_endOfPeak + 1;
else
% found the end of the peak
break;
end
end
% write down the end of the peak
resPeaksPart(numbPeaksPart, colPeakEnd) = ...
timePart(indFD_endOfPeak);
%==================
% STEP 3e.
% check if the SD in the negative zone has more than 1 dip,
% if so then we have a case of strong co-elusion, and
% require a split of this peak into the seperate peaks
% first calculate the number of change of sign in the
% third derivative
% i. get the third derivative values in the negative zone
smdTDinNegZone = smdTD(indSD_NegZoneSta(nZone):indSD_NegZoneEnd(nZone));
% ii. get logical index of TD values greater than 0 (+ve
% and -ve values of TD), any difference between consequent
% indices that's not 0 shows there's a change in sign
indChangeInSignTD = find(diff(smdTDinNegZone > 0));
% iii. count the number of change in sign
nChangeInSignTD = length(indChangeInSignTD);
% iv. calculate the number of minimum in the SD
if mod(nChangeInSignTD, 2)
% if n is odd
nDipsInSD = (nChangeInSignTD + 1) / 2;
else
% if n is even
% nb. don't know how this could happen but I'll leave
% this in here
nDipsInSD = nChangeInSignTD / 2;
end
% If there are more than one dips in the SD -ve zone, then
% we'll need to split the current peak
if nDipsInSD > 1 && splitCoeultion
% set aside another matrix for these results
multiPeakZoneRes = zeros(nDipsInSD, 5);
% the start and end of the peak region now goes into
% the start of peak 1 and end of last peak
multiPeakZoneRes(1, colPeakStart) = ...
resPeaksPart(numbPeaksPart, colPeakStart);
multiPeakZoneRes(nDipsInSD, colPeakEnd) = ...
resPeaksPart(numbPeaksPart, colPeakEnd);
% keep track the indices for the start and end
mpi1 = zeros(nDipsInSD, 1);
mpi2 = zeros(nDipsInSD, 1);
mpi1(1) = indFD_startOfPeak;
mpi2(end) = indFD_endOfPeak;
% v. find all the minimum SD in the -ve zone, these
% will be the peak maxima, this is when the TD change
% from -ve to +ve
indMinsSD = find(diff(smdTDinNegZone > 0) == 1);
indPeakMaxInMultiZone = indSD_NegZoneSta(nZone)+indMinsSD-1;
multiPeakZoneRes(:, colPeakMax) = timePart(indPeakMaxInMultiZone)';
multiPeakZoneRes(:, colPeakHeight) = smdZD(indPeakMaxInMultiZone)';
% vi. when the TD change from +ve to -ve, that's when
% the split should be
indMaxsSD = find(diff(smdTDinNegZone > 0) == -1);
indPeakSplit = indSD_NegZoneSta(nZone)+indMaxsSD-1;
if ~mod(nChangeInSignTD, 2)
% if n is even, then we need to make sure the split
% happens after the peak
indPeakSplit_indActual = ...
find(indPeakSplit > indPeakMaxInMultiZone(1));
indPeakSplit = indPeakSplit(indPeakSplit_indActual);
end
multiPeakZoneRes(1:nDipsInSD-1, colPeakEnd) = ...
timePart(indPeakSplit)';
multiPeakZoneRes(2:nDipsInSD, colPeakStart) = ...
timePart(indPeakSplit)';
mpi1(2:nDipsInSD) = indPeakSplit;
mpi2(1:nDipsInSD-1) = indPeakSplit;
%==================
% STEP 3f. calculate the area under the curve
for nDip = 1 : nDipsInSD
multiPeakZoneRes(nDip, colPeakArea) = ...
calcAUC( smdZD( mpi1(nDip):mpi2(nDip) ), ...
timePart( mpi1(nDip):mpi2(nDip) ) );
end
% write the whole temporary matrix into the matrix for
% this partition's result
resPeaksPart(numbPeaksPart:numbPeaksPart+nDipsInSD-1, :) = ...
multiPeakZoneRes;
% update the number of peaks found in this partition
numbPeaksPart = numbPeaksPart + nDipsInSD - 1;
else
% if there's only one dip
%==================
% STEP 3f. calculate the area under the curve
% first check that the peak is not just one point, if
% it is, then delete the current row, and decrement the
% count
if length(smdZD(indFD_startOfPeak:indFD_endOfPeak)) > 1
areaPeak = calcAUC(smdZD(indFD_startOfPeak:indFD_endOfPeak), ...
timePart(indFD_startOfPeak:indFD_endOfPeak));
% write down the area under the peak
resPeaksPart(numbPeaksPart, colPeakArea) = areaPeak;
else
resPeaksPart(numbPeaksPart, :) = [];
numbPeaksPart = numbPeaksPart - 1;
end
end
end % end if : the -ve zone is valid for peak
end % end for : all the -ve zones in this partition
% plot all the peaks in this partition on the figure
if showPlot
figure(hFigPart);
propsMarker = {'MarkerSize', 12};
plot(resPeaksPart(:, colPeakStart), zeros(numbPeaksPart, 1), ...
'm^', propsMarker{:}, 'MarkerFaceColor', 'm');
plot(resPeaksPart(:, colPeakEnd), zeros(numbPeaksPart, 1), ...
'rv', propsMarker{:}, 'MarkerFaceColor', 'r');
plot(resPeaksPart(:, colPeakMax), zeros(numbPeaksPart, 1), ...
'go', propsMarker{:}, 'MarkerFaceColor', 'g');
end
% Output number of peaks found in the partition
fprintf('Partition number %d, number of peaks found: %d. ', ...
partNumb, numbPeaksPart);
if showPlot
fprintf('Press any key to continue. \n');
pause;
else
fprintf('\n');
end
% update peaks for the full chromatogram
NPeaksTotal = NPeaksTotal + numbPeaksPart;
resPeaks = [resPeaks; resPeaksPart];
end % end of peak detection for each partition
end % analysed all data presented.
if showPlot
% plot all the peaks on the full signal
figure(hFig);
clf;
hold on;
plot(timesteps, gcData, props{:});
set(gca, 'YLim', [0 yULim]);
grid on;
propsMarker = {'MarkerSize', 8};
plot(resPeaks(:, colPeakStart), zeros(NPeaksTotal, 1), ...
'm^', propsMarker{:}, 'MarkerFaceColor', 'm');
plot(resPeaks(:, colPeakEnd), zeros(NPeaksTotal, 1), ...
'rv', propsMarker{:}, 'MarkerFaceColor', 'r');
plot(resPeaks(:, colPeakMax), zeros(NPeaksTotal, 1), ...
'go', propsMarker{:}, 'MarkerFaceColor', 'g');
end
fprintf('------------------\n');
fprintf('Total number of peaks found: %d. \n', NPeaksTotal);
%%-------------------------------------
% subfunction to calculate the noise of a signal.
% The noise is the median of all abolute differences between the signal
% at i and the mean of its immediate neighbours i-1 and i+1
function noiseVal = calcNoise(signal)
neighbour1 = signal(1:end-2);
neighbour2 = signal(3:end);
meanNeighbours = (neighbour1 + neighbour2) / 2;
diffWithNeighbour = signal(2:end-1) - meanNeighbours;
noiseVal = median(abs(diffWithNeighbour));
%%-------------------------------------
% subfunction to calculate the area under the curve of a signal.
% The area is calculated using the Trapezoidal rule since some of the
% peaks are very sharp to use first principle.
% The inputs are the part of the signal with the peak, and the elution
% time or the timesteps corresponding to the signal
function resArea = calcAUC(signal, etime)
val1 = signal(1:end-1);
val2 = signal(2:end);
incTime = diff(etime);
resArea = sum((val1 + val2) .* incTime ./ 2);
%%-------------------------------------
% subfunction to partition the whole signal
function [partStIndex, partEndIndex] = partitionSignal(smdInitial, ...
thrSig, N, splitSignalSize)
nPart = ceil(N/splitSignalSize);
partStIndex = zeros(nPart, 1);
k = 1;
partStIndex(k) = 1;
flgPartition = 1;
while flgPartition
k = k + 1;
% get to the next start point
stNext = partStIndex(k-1) + splitSignalSize;
% check if this point and it's surrounding 10 points are all below
% the threshold, if not, then go to the next point along the line
% and search until a section is found.
surrPoints = 10;
while true
%secVal = smdInitial(stNext-surrPoints : stNext+surrPoints);
if smdInitial(stNext-surrPoints : stNext+surrPoints) < thrSig
break;
else
stNext = stNext + 1;
end
% make sure that the index stNext is not near the end of the
% data
if stNext+surrPoints >= N
stNext = 0;
break;
end
end
partStIndex(k) = stNext;
% check if the number of points reminding is smaller than
% splitSignalSize or not, exit while loop if true
if N - stNext - surrPoints <= splitSignalSize || stNext == 0
flgPartition = 0;
break;
end
end
% make sure there's no zeros in the indices, delete these if so
partStIndex(find(partStIndex == 0)) = []; %#ok<FNDSB>
% the indices for the end of the partitions
partEndIndex = [partStIndex(2:end)-1; N];