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add missing .m files for MAIN

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L. Dijk 2021-07-03 16:37:53 +02:00
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commit c64768e2bd
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ControlsData.mat Normal file
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ControlsDetermineLocationTurnsFunc.m Normal file
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function [locsTurns,FilteredData,FootContacts] = ControlsDetermineLocationTurnsFunc(inputData,FS,ApplyRealignment,plotit,ResultStruct)
% Description: Determine the location of turns, plot for visual inspection
% Input: Acc Data (not yet realigned)
%Realign sensor data to VT-ML-AP frame
if ApplyRealignment % apply relignment as described in Rispens S, Pijnappels M, van Schooten K, Beek PJ, Daffertshofer A, van Die?n JH (2014).
data = inputData(:,[3,2,1]); % NOT THE SAME AS IN THE CLBP DATA; reorder data to 1 = V; 2 = ML; 3 = AP
% Consistency of gait characteristics as determined from acceleration data collected at different trunk locations. Gait Posture 2014;40(1):187-92.
[RealignedAcc, ~] = RealignSensorSignalHRAmp(data, FS);
dataAcc = RealignedAcc;
else
data = inputData; % Realignment performed in previous stage
dataAcc = inputData;
end
% Filter data
[B,A] = butter(2,20/(FS/2),'low'); % Filters data very strongly which is needed to determine turns correctly
dataStepDetection = filtfilt(B,A,dataAcc);
VTAcc = data(:,1);
APAcc = data(:,3);
%% Determine Steps -
% USE THE AP ACCELERATION: WIEBREN ZIJLSTRA: ASSESSMENT OF SPATIO-TEMPORAL PARAMTERS DURING UNCONSTRAINED WALKING (2004)
% In order to run the step detection script we first need to run an autocorrelation function;
StrideTimeRange = [0.2 4.0]; % Range to search for stride time (seconds)
[ResultStruct] = AutocorrStrides(dataStepDetection,FS, StrideTimeRange,ResultStruct); % first guess of stridetimesamples
% StrideTimeSamples is needed as an input for the stepcountFunc;
StrideTimeSamples = ResultStruct.StrideTimeSamples;
[PksAndLocsCorrected] = StepcountFunc(data,StrideTimeSamples,FS);
FootContacts = PksAndLocsCorrected; % (1:2:end,2); previous version
numStepsOption2_filt = numel(FootContacts); % counts number of steps;
%% Determine Turns
% To convert the XYZ acceleration vectors at each point in time into scalar values,
% calculate the magnitude of each vector. This way, you can detect large changes in overall acceleration,
% such as steps taken while walking, regardless of device orientation.
magfilt = sqrt(sum((dataStepDetection(:,1).^2) + (dataStepDetection(:,2).^2) + (dataStepDetection(:,3).^2), 2));
magNoGfilt = magfilt - mean(magfilt);
minPeakHeight2 = 1*std(magNoGfilt); % used to be 2 % based on visual inspection, parameter tuning was performed on *X*standard deviation from MInPeak (used to be 1 SD)
[pks, locs] = findpeaks(magNoGfilt, 'MINPEAKHEIGHT', minPeakHeight2,'MINPEAKDISTANCE',0.3*FS); % for step detection
numStepsOption2_filt = numel(pks); % counts number of locs for turn detection
diffLocs = diff(locs); % calculates difference in location magnitude differences
avg_diffLocs = mean(diffLocs); % average distance between steps
std_diffLocs = std(diffLocs); % standard deviation of distance between steps
figure;
findpeaks(diffLocs, 'MINPEAKHEIGHT', avg_diffLocs, 'MINPEAKDISTANCE',0.2*FS); % these values have been chosen based on visual inspection of the signal
line([1 length(diffLocs)],[avg_diffLocs avg_diffLocs])
[pks_diffLocs, locs_diffLocs] = findpeaks(diffLocs, 'MINPEAKHEIGHT', avg_diffLocs,'MINPEAKDISTANCE',0.2*FS); % values were initially 5
locsTurns = [locs(locs_diffLocs), locs(locs_diffLocs+1)];
%magNoGfilt_copy = magNoGfilt;
VTAcc_copy = data(:,1);
APAcc_copy = data(:,3);
for k = 1: size(locsTurns,1);
VTAcc_copy(locsTurns(k,1):locsTurns(k,2)) = NaN;
APAcc_copy(locsTurns(k,1):locsTurns(k,2)) = NaN;
end
% Visualising signal;
if plotit
figure()
subplot(2,1,1)
hold on;
plot(VTAcc,'b')
plot(VTAcc_copy, 'r');
title('Inside Straight: Filtered data VT with turns highlighted in blue')
line([6000,12000,18000,24000,30000,36000;6000,12000,18000,24000,30000,36000],[5,5,5,5,5,5;10,10,10,10,10,10],'LineWidth',2,'Linestyle','--','color','k')
hold on;
subplot(2,1,2)
plot(APAcc,'g')
plot(APAcc_copy, 'r');
title('Inside Straight: Filtered data AP with turns highlighted in blue')
line([6000,12000,18000,24000,30000,36000;6000,12000,18000,24000,30000,36000],[0,0,0,0,0,0;10,10,10,10,10,10],'LineWidth',2,'Linestyle','--','color','k')
hold off;
end
% Check if number of turns * 20 m are making sense based on total
% distance measured by researcher.
disp(['Number of turns detected = ' num2str(size(locsTurns,1))])
%disp(['Total distance measured by researcher was = ' num2str(Distance)])
FilteredData = dataAcc;
end

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FINAL_MAP_CLBP_Controls_23052021.xls Normal file
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FINAL_NPRSBaseline_Minute_23052021.xls Normal file
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FINAL_NPRS_GaitCharacteristics_23052021.xls Normal file
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FalseNearestNeighborsSR.m Normal file
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function fnnM = FalseNearestNeighborsSR(xV,tauV,mV,escape,theiler)
% fnnM = FalseNearestNeighbors(xV,tauV,mV,escape,theiler)
% FALSENEARESTNEIGHBORS computes the percentage of false nearest neighbors
% for a range of delays in 'tauV' and embedding dimensions in 'mV'.
% INPUT
% xV : Vector of the scalar time series
% tauV : A vector of the delay times.
% mV : A vector of the embedding dimension.
% escape : A factor of escaping from the neighborhood. Default=10.
% theiler : the Theiler window to exclude time correlated points in the
% search for neighboring points. Default=0.
% OUTPUT:
% fnnM : A matrix of size 'ntau' x 'nm', where 'ntau' is the number of
% given delays and 'nm' is the number of given embedding
% dimensions, containing the percentage of false nearest
% neighbors.
%========================================================================
% <FalseNearestNeighbors.m>, v 1.0 2010/02/11 22:09:14 Kugiumtzis & Tsimpiris
% This is part of the MATS-Toolkit http://eeganalysis.web.auth.gr/
%========================================================================
% Copyright (C) 2010 by Dimitris Kugiumtzis and Alkiviadis Tsimpiris
% <dkugiu@gen.auth.gr>
%========================================================================
% Version: 1.0
% LICENSE:
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 3 of the License, or
% any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see http://www.gnu.org/licenses/>.
%=========================================================================
% Reference : D. Kugiumtzis and A. Tsimpiris, "Measures of Analysis of Time Series (MATS):
% A Matlab Toolkit for Computation of Multiple Measures on Time Series Data Bases",
% Journal of Statistical Software, in press, 2010
% Link : http://eeganalysis.web.auth.gr/
%=========================================================================
% Updates:
% Sietse Rispens, January 2012: use a different kdtree algorithm,
% searching k nearest neighbours, to improve performance
%
%=========================================================================
fthres = 0.1; % A factor of the data SD to be used as the maximum radius
% for searching for valid nearest neighbor.
propthres = fthres; % Limit for the proportion of valid points, i.e. points
% for which a nearest neighbor was found. If the proporion
% of valid points is beyond this limit, do not compute
% FNN.
n = length(xV);
if isempty(escape), escape=10; end
if isempty(theiler), theiler=0; end
% Rescale to [0,1] and add infinitesimal noise to have distinct samples
xmin = min(xV);
xmax = max(xV);
xV = (xV - xmin) / (xmax-xmin);
xV = AddNoise(xV,10^(-10));
ntau = length(tauV);
nm = length(mV);
fnnM = NaN*ones(ntau,nm);
for itau = 1:ntau
tau = tauV(itau);
for im=1:nm
m = mV(im);
nvec = n-m*tau; % to be able to add the component x(nvec+tau) for m+1
if nvec-theiler < 2
break;
end
xM = NaN*ones(nvec,m);
for i=1:m
xM(:,m-i+1) = xV(1+(i-1)*tau:nvec+(i-1)*tau);
end
% k-d-tree data structure of the training set for the given m
TreeRoot=kdtree_build(xM);
% For each target point, find the nearest neighbor, and check whether
% the distance increase over the escape distance by adding the next
% component for m+1.
idxV = NaN*ones(nvec,1);
distV = NaN*ones(nvec,1);
k0 = 2; % The initial number of nearest neighbors to look for
kmax = min(2*theiler + 2,nvec); % The maximum number of nearest neighbors to look for
for i=1:nvec
tarV = xM(i,:);
iV = [];
k=k0;
kmaxreached = 0;
while isempty(iV) && ~kmaxreached
[neiindV, neidisV] = kdtree_k_nearest_neighbors(TreeRoot,tarV,k);
% [neiM,neidisV,neiindV]=kdrangequery(TreeRoot,tarV,rthres*sqrt(m));
[oneidisV,oneiindV]=sort(neidisV);
neiindV = neiindV(oneiindV);
neidisV = neidisV(oneiindV);
iV = find(abs(neiindV(1)-neiindV(2:end))>theiler);
if k >= kmax
kmaxreached = 1;
elseif isempty(iV)
k = min(kmax,k*2);
end
end
if ~isempty(iV)
idxV(i) = neiindV(iV(1)+1);
distV(i) = neidisV(iV(1)+1);
end
end % for i
iV = find(~isnan(idxV));
nproper = length(iV);
% Compute fnn only if there is a sufficient number of target points
% having nearest neighbor (in R^m) within the threshold distance
if nproper>propthres*nvec
nnfactorV = 1+(xV(iV+m*tau)-xV(idxV(iV)+m*tau)).^2./distV(iV).^2;
fnnM(itau,im) = length(find(nnfactorV > escape^2))/nproper;
end
kdtree_delete(TreeRoot); % Free the pointer to k-d-tree
end
end

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GaitOutcomesTrunkAccFuncLD.m Normal file
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function [ResultStruct] = GaitOutcomesTrunkAccFuncLD(inputData,FS,LegLength,WindowLen,ApplyRealignment,ApplyRemoveSteps)
% Description: Trunk analysis of Iphone data without the need for step detection
% CL Nov 2019
% Adapted IH feb-april 2020
% koloms data of smartphone
% 1st column is time data;
% 2nd column is X, medio-lateral: + left, - right
% 3rd column is Y, vertical: + downwards, - upwards
% 4th column is Z, anterior- posterior : + forwards, - backwards
%% Input Trunk accelerations during locomotion in VT, ML, AP direction
% InputData: Acceleration signal with time and accelerations in VT,ML and
% AP direction.
% FS: sample frequency of the Accdata
% LegLength: length of the leg of the participant in m;
%% Output
% ResultStruct: structure coninting all outcome measured calculated
% Spectral parameters, spatiotemporal gait parameters, non-linear
% parameters
% fields and subfields: include the multiple measurements of a subject
%% Literature
% Richman & Moorman, 2000; [ sample entropy]
% Bisi & Stagni Gait & Posture 2016, 47 (6) 37-42
% Kavagnah et al., Eur J Appl Physiol 2005 94: 468?475; Human Movement Science 24(2005) 574?587 [ synchrony]
% Moe-Nilsen J Biomech 2004 37, 121-126 [ autorcorrelation step regularity and symmetry
% Kobsar et al. Gait & Posture 2014 39, 553?557 [ synchrony ]
% Rispen et al; Gait & Posture 2014, 40, 187 - 192 [realignment axes]
% Zijlstra & HofGait & Posture 2003 18,2, 1-10 [spatiotemporal gait variables]
% Lamoth et al, 2002 [index of harmonicity]
% Costa et al. 2003 Physica A 330 (2003) 53–60 [ multiscale entropy]
% Cignetti F, Decker LM, Stergiou N. Ann Biomed Eng. 2012
% May;40(5):1122-30. doi: 10.1007/s10439-011-0474-3. Epub 2011 Nov 25. [
% Wofl vs. Rosenstein Lyapunov]
%% Settings
Gr = 9.81; % Gravity acceleration, multiplication factor for accelerations
StrideFreqEstimate = 1.00; % Used to set search for stride frequency from 0.5*StrideFreqEstimate until 2*StrideFreqEstimate
StrideTimeRange = [0.2 4.0]; % Range to search for stride time (seconds)
IgnoreMinMaxStrides = 0.10; % Number or percentage of highest&lowest values ignored for improved variability estimation
N_Harm = 12; % Number of harmonics used for harmonic ratio, index of harmonicity and phase fluctuation
LowFrequentPowerThresholds = ...
[0.7 1.4]; % Threshold frequencies for estimation of low-frequent power percentages
Lyap_m = 7; % Embedding dimension (used in Lyapunov estimations)
Lyap_FitWinLen = round(60/100*FS); % Fitting window length (used in Lyapunov estimations Rosenstein's method)
Sen_m = 5; % Dimension, the length of the subseries to be matched (used in sample entropy estimation)
Sen_r = 0.3; % Tolerance, the maximum distance between two samples to qualify as match, relative to std of DataIn (used in sample entropy estimation)
NStartEnd = [100];
M = 5; % maximum template length
ResultStruct = struct();
%% Filter and Realign Accdata
% Apply Realignment & Filter data
if ApplyRealignment % apply relignment as described in Rispens S, Pijnappels M, van Schooten K, Beek PJ, Daffertshofer A, van Die?n JH (2014).
data = inputData(:, [3,2,4]); % reorder data to 1 = V; 2= ML, 3 = AP%
% Consistency of gait characteristics as determined from acceleration data collected at different trunk locations. Gait Posture 2014;40(1):187-92.
[RealignedAcc, ~] = RealignSensorSignalHRAmp(data, FS);
dataAcc = RealignedAcc;
[B,A] = butter(2,20/(FS/2),'low');
dataAcc_filt = filtfilt(B,A,dataAcc);
else % we asume tat data is already reorderd to 1 = V; 2= ML, 3 = AP in an earlier stage;
[B,A] = butter(2,20/(FS/2),'low');
dataAcc = inputData;
dataAcc_filt = filtfilt(B,A,dataAcc);
end
%% Step dectection
% Determines the number of steps in the signal so that the first 30 and last 30 steps in the signal can be removed
if ApplyRemoveSteps
% In order to run the step detection script we first need to run an autocorrelation function;
[ResultStruct] = AutocorrStrides(dataAcc_filt,FS, StrideTimeRange,ResultStruct);
% StrideTimeSamples is needed as an input for the stepcountFunc;
StrideTimeSamples = ResultStruct.StrideTimeSamples;
% Calculate the number of steps;
[PksAndLocsCorrected] = StepcountFunc(dataAcc_filt,StrideTimeSamples,FS);
% This function selects steps based on negative and positive values.
% However to determine the steps correctly we only need one of these;
LocsSteps = PksAndLocsCorrected(1:2:end,2);
%% Cut data & remove currents results
% Remove 1 step in the beginning and end of data (comment Bert Otten)
dataAccCut = dataAcc(LocsSteps(1):LocsSteps(end-1),:);
dataAccCut_filt = dataAcc_filt(LocsSteps(1):LocsSteps(end-1),:);
% Clear currently saved results from Autocorrelation Analysis
clear ResultStruct;
clear PksAndLocsCorrected;
clear LocsSteps;
else;
dataAccCut = dataAcc;
dataAccCut_filt = dataAcc_filt;
end
%% Calculate stride parameters
ResultStruct = struct; % create empty struct
% Run function AutoCorrStrides, Outcomeparameters: StrideRegularity,RelativeStrideVariability,StrideTimeSamples,StrideTime
[ResultStruct] = AutocorrStrides(dataAccCut_filt,FS, StrideTimeRange,ResultStruct);
StrideTimeSamples = ResultStruct.StrideTimeSamples; % needed as input for other functions
% Calculate Step symmetry --> method 1
ij = 1;
dirSymm = [1,3]; % Gait Synmmetry is only informative in AP/V direction: See Tura A, Raggi M, Rocchi L, Cutti AG, Chiari L: Gait symmetry and regularity in transfemoral amputees assessed by trunk accelerations. J Neuroeng Rehabil 2010, 7:4.
for jk=1:length(dirSymm)
[C, lags] = AutocorrRegSymmSteps(dataAccCut_filt(:,dirSymm(jk)));
[Ad,p] = findpeaks(C,'MinPeakProminence',0.2, 'MinPeakHeight', 0.2);
if size(Ad,1) > 1
Ad1 = Ad(1);
Ad2 = Ad(2);
GaitSymm(:,ij) = abs((Ad1-Ad2)/mean([Ad1+Ad2]))*100;
else
GaitSymm(:,ij) = NaN;
end
ij = ij +1;
end
% Save outcome in struct;
ResultStruct.GaitSymm_V = GaitSymm(1);
ResultStruct.GaitSymm_AP = GaitSymm(2);
% Calculate Step symmetry --> method 2
[PksAndLocsCorrected] = StepcountFunc(dataAccCut_filt,StrideTimeSamples,FS);
LocsSteps = PksAndLocsCorrected(2:2:end,2);
if rem(size(LocsSteps,1),2) == 0; % is number of steps is even
LocsSteps2 = LocsSteps(1:2:end);
else
LocsSteps2 = LocsSteps(3:2:end);
end
LocsSteps1 = LocsSteps(2:2:end);
DiffLocs2 = diff(LocsSteps2);
DiffLocs1 = diff(LocsSteps1);
StepTime2 = DiffLocs2(1:end-1)/FS; % leave last one out because it is higher
StepTime1 = DiffLocs1(1:end-1)/FS;
SI = abs((2*(StepTime2-StepTime1))./(StepTime2+StepTime1))*100;
ResultStruct.GaitSymmIndex = nanmean(SI);
%% Calculate spatiotemporal stride parameters
% Measures from height variation by double integration of VT accelerations and high-pass filtering
[ResultStruct] = SpatioTemporalGaitParameters(dataAccCut_filt,StrideTimeSamples,ApplyRealignment,LegLength,FS,IgnoreMinMaxStrides,ResultStruct);
%% Measures derived from spectral analysis
AccVectorLen = sqrt(sum(dataAccCut_filt(:,1:3).^2,2));
[ResultStruct] = SpectralAnalysisGaitfunc(dataAccCut_filt,WindowLen,FS,N_Harm,LowFrequentPowerThresholds,AccVectorLen,ResultStruct);
%% Calculation non-linear parameters;
% cut into windows of size WindowLen
N_Windows = floor(size(dataAccCut,1)/WindowLen);
N_SkipBegin = ceil((size(dataAccCut,1)-N_Windows*WindowLen)/2);
LyapunovWolf = nan(N_Windows,3);
LyapunovRosen = nan(N_Windows,3);
SE= nan(N_Windows,3);
for WinNr = 1:N_Windows;
AccWin = dataAccCut(N_SkipBegin+(WinNr-1)*WindowLen+(1:WindowLen),:);
for j=1:3
[LyapunovWolf(WinNr,j),~] = CalcMaxLyapWolfFixedEvolv(AccWin(:,j),FS,struct('m',Lyap_m));
[LyapunovRosen(WinNr,j),outpo] = CalcMaxLyapConvGait(AccWin(:,j),FS,struct('m',Lyap_m,'FitWinLen',Lyap_FitWinLen));
[SE(WinNr,j)] = funcSampleEntropy(AccWin(:,j), Sen_m, Sen_r);
% no correction for FS; SE does increase with higher FS but effect is considered negligible as range is small (98-104HZ). Might consider updating r to account for larger ranges.
end
end
LyapunovWolf = nanmean(LyapunovWolf,1);
LyapunovRosen = nanmean(LyapunovRosen,1);
SampleEntropy = nanmean(SE,1);
ResultStruct.LyapunovWolf_V = LyapunovWolf(1);
ResultStruct.LyapunovWolf_ML = LyapunovWolf(2);
ResultStruct.LyapunovWolf_AP = LyapunovWolf(3);
ResultStruct.LyapunovRosen_V = LyapunovRosen(1);
ResultStruct.LyapunovRosen_ML = LyapunovRosen(2);
ResultStruct.LyapunovRosen_AP = LyapunovRosen(3);
ResultStruct.SampleEntropy_V = SampleEntropy(1);
ResultStruct.SampleEntropy_ML = SampleEntropy(2);
ResultStruct.SampleEntropy_AP = SampleEntropy(3);
if isfield(ResultStruct,'StrideFrequency')
LyapunovPerStrideWolf = LyapunovWolf/ResultStruct.StrideFrequency;
LyapunovPerStrideRosen = LyapunovRosen/ResultStruct.StrideFrequency;
end
ResultStruct.LyapunovPerStrideWolf_V = LyapunovPerStrideWolf(1);
ResultStruct.LyapunovPerStrideWolf_ML = LyapunovPerStrideWolf(2);
ResultStruct.LyapunovPerStrideWolf_AP = LyapunovPerStrideWolf(3);
ResultStruct.LyapunovPerStrideRosen_V = LyapunovPerStrideRosen(1);
ResultStruct.LyapunovPerStrideRosen_ML = LyapunovPerStrideRosen(2);
ResultStruct.LyapunovPerStrideRosen_AP = LyapunovPerStrideRosen(3);
end

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GaitVarOutcomesCombined_230221.mat Normal file
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Hratio.m Normal file
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function [Hratio,wb]=Hratio(x,fmax,numfreq)
% function [HIndex]=IndexOfHarmonicity(x,numfreq);
%
% INPUT, signal, fmax is max frequency that can be considered as main
% frequency = around 1 for stride and around 2 for steps.
% numfreq = number of superharmonics in analysis
% OUTPUT: Harmoncity Index and mainfrequency
% PLOT: with no output a plot is generated
% CALLS: WndMainFreq.m
% CL 2016
if nargin<3 || isempty(numfreq), numfreq = 10; end
fs = 100;% sample frequency
le=length(x);
temp=[];
n=10*length(x);
ws=fix(length(x)/2);
no=fix(0.99*ws);
[Px,fx]=spectrum2(x,n,no,boxcar(le),100,'mean');
Px = Px/sum(Px); % All power spectral densities were normalized by dividing the power by the sum of the total power spectrum, which equals the variance.
% select frequency
wb = WindMainFreq(x,100,fmax) ; % mainfrequency frequency
wbr= wb + 0.055; % % basis mainfrequency + tail
wbl = wb - 0.055;
wind=find(fx >=wbl & fx<= wbr); % index van basisfrequentie
PI_0=sum(Px(wind));
temp=PI_0;
for k=1:numfreq;
w=wb*(k+1);
wr=w+0.055;
wl=w-0.055;
wInd=find(fx >=wl & fx<=wr);
if nargout ==0; % controle
plot(fx,Px,'r'); hold on;
set(gca','XLim', [0 6],'FontSize', 8)
xlabel('Frequency (Hz)'); ylabel('Power');
plot(wb,max(Px),'r.','MarkerSize', 10),
plot(wbr,0,'c.'); plot(wbl,0,'c.');
plot(w,0,'r.','MarkerSize', 10)
plot(wl,0,'c.'); plot(wr,0,'c.');
end
PI=sum(Px(wInd));
temp=[temp; PI];
end
Hratio = sum(temp(1:2:end-1))/sum(temp(2:2:end));

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IndexOfHarmonicity.m Normal file
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function [HIndex,wb]=IndexOfHarmonicity(x,fmax,numfreq)
% function [HIndex]=IndexOfHarmonicity(x,numfreq);
%
% INPUT, signal, fmax is max frequency that can be considered as main
% frequency = around 1 for stride and around 2 for steps.
% numfreq = number of superharmonics in analysis
% OUTPUT: Harmoncity Index and mainfrequency
% PLOT: with no output a plot is generated
% CALLS: WndMainFreq.m
% CL 2016
if nargin<3 || isempty(numfreq), numfreq = 10; end
fs = 100;% sample frequency
le=length(x);
temp=[];
n=10*length(x);
ws=fix(length(x)/2);
no=fix(0.99*ws);
[Px,fx]=spectrum2(x,n,no,boxcar(le),100,'mean');
Px = Px/sum(Px); % All power spectral densities were normalized by dividing the power by the sum of the total power spectrum, which equals the variance.
% select frequency
wb = WindMainFreq(x,100,fmax) ; % mainfrequency frequency
wbr= wb + 0.055; % % basis mainfrequency + tail
wbl = wb - 0.055;
wind=find(fx >=wbl & fx<= wbr); % index van basisfrequentie
PI_0=sum(Px(wind));
temp=PI_0;
for k=1:numfreq;
w=wb*(k+1);
wr=w+0.055;
wl=w-0.055;
wInd=find(fx >=wl & fx<=wr);
if nargout ==0; % controle
plot(fx,Px,'r'); hold on;
set(gca','XLim', [0 6],'FontSize', 8)
xlabel('Frequency (Hz)'); ylabel('Power');
plot(wb,max(Px),'r.','MarkerSize', 10),
plot(wbr,0,'c.'); plot(wbl,0,'c.');
plot(w,0,'r.','MarkerSize', 10)
plot(wl,0,'c.'); plot(wr,0,'c.');
end
PI=sum(Px(wInd));
temp=[temp; PI];
end
HIndex=PI_0/sum(temp);

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WindMainFreq.m Normal file
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function Omega=WindMainFreq(x,fs,fmax);
% function Omega=WindMainFreq(x,fs,fmax);
%INPUT: x = signal; fs = sample frequency; fmax = max frequency for
%mainfrequency
% OUTPUT = mainfrequency Omega
% CALSS: spectrum2.m
% PLOT : with no outtput [] generates plot
if nargin<3 || isempty(fmax), fmax = 4; end
n=10*length(x);
ws=fix(length(x)/2);
no=fix(0.99*ws);
[p,f]=spectrum2(x,n,no,hamming(ws),fs,'mean');
p=p/sum(p);
aa=find(f>0.5 & f<fmax);
[a,b]=max(p(aa));
Omega=f(b+aa(1)-1);
if nargout ==0;
ii=find(f(:,1)<=fmax);
f=f(1:length(ii),:);
p=p(1:length(ii),:);
plot(f,p,'b');hold on;
plot(Omega,max(p(aa)),'m.','MarkerSize', 15); %check w0
end

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function [e,A,B]=cross_sampen(x,y,M,r,sflag);
%function [e,A,B]=cross_sampen(x,y,M,r);
%
% The Cross-sample Entropy (Cross-SampEn) quantified the degree of synchronization between AP and ML, AP and V, and ML and V accelerations.
% Cross-SampEn is the negative natural logarithm of the conditional probability that epochs with length m that match point-wise
% in the two related signals, repeat itself for m+1 points, within a tolerance of r (in the present study m = 5 and r = 0.3)
%Input
%
%x,y input data
%M maximum template length
%r matching tolerance
%sflag flag to standardize signals(default yes/sflag=1)
%
%Output
%
%e sample entropy estimates for m=0,1,...,M-1
%A number of matches for m=1,...,M
%B number of matches for m=0,...,M-1 excluding last point
if ~exist('sflag')|isempty(sflag),sflag=1;end
y=y(:);
x=x(:);
ny=length(y);
nx=length(x);
N=nx;
if sflag>0
y=y-mean(y);
sy=sqrt(mean(y.^2));
y=y/sy;
x=x-mean(x);
sx=sqrt(mean(x.^2));
x=x/sx;
end
lastrun=zeros(nx,1);
run=zeros(nx,1);
A=zeros(M,1);
B=zeros(M,1);
p=zeros(M,1);
e=zeros(M,1);
for i=1:ny
for j=1:nx
if abs(x(j)-y(i))<r
run(j)=lastrun(j)+1;
M1=min(M,run(j));
for m=1:M1
A(m)=A(m)+1;
if (i<ny)&(j<nx)
B(m)=B(m)+1;
end
end
else
run(j)=0;
end
end
for j=1:nx
lastrun(j)=run(j);
end
end
N=ny*nx;
B=[N;B(1:(M-1))];
p=A./B;
e=-log(p);

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% Function for calculating multiscale entropy
% input: signal
% m: match point(s)
% r: matching tolerance
% factor: number of scale factor
% sampenc is available at http://people.ece.cornell.edu/land/PROJECTS/Complexity/sampenc.m
%
% Multi-scale sample Entropy (Mscale-En) is an indicator of gait predictability. Multi-scale entropy takes the
% complexity of a system into account by calculating the
% predictability of a signal over time scales with increasing
% length. A ‘coarse-graining’ process is applied to the acceleration signals; non-overlapping windows of data
% points with an increasing length τ are constructed, with
% τ representing the time scale with a tolerance of r (in the
% present study τ = 7 and r = 0.2). A complete predictable
% signal will adopt a Mscale-En value of 0 [29].
function e = msentropy(input,m,r,factor)
y=input;
y=y-mean(y);
y=y/std(y);
for i=1:factor
s=coarsegraining(y,i); % dont have this function yet.
sampe=sampenc(s,m+1,r);
e(i)=sampe(m+1);
end
e=e';

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function [Spec,f,SpecConf] = spectrum2(varargin)
%SPECTRUM Power spectrum estimate of one or two data sequences.
% P=SPECTRUM2(X,NFFT,NOVERLAP,WIND) estimates the Power Spectral Density of
% signal vector(s) X using Welch's averaged periodogram method. X must be a
% set of column vectors. They are divided into overlapping sections, each of
% which is detrended and windowed by the WINDOW parameter, then zero padded
% to length NFFT. The magnitude squared of the length NFFT DFTs of the sec-
% tions are averaged to form Pxx. P is a two times SIZE(X,2) column matrix
% P = [Pxx Pxxc]; the second half of columns Pxxc are the 95% confidence
% intervals. The number of rows of P is NFFT/2+1 for NFFT even, (NFFT+1)/2
% for NFFT odd, or NFFT if the signal X is complex. If you specify a scalar
% for WINDOW, a Hanning window of that length is used.
%
% [P,F] = SPECTRUM2(X,NFFT,NOVERLAP,WINDOW,Fs) given a sampling frequency
% Fs returns a vector of frequencies the same length as Pxx at which the
% PSD is estimated. PLOT(F,P(:,1:end/2)) plots the power spectrum estimate
% versus true frequency.
%
% [P, F] = SPECTRUM2(X,NFFT,NOVERLAP,WINDOW,Fs,Pr) where Pr is a scalar
% between 0 and 1, overrides the default 95% confidence interval and
% returns the Pr*100% confidence interval for Pxx instead.
%
% SPECTRUM2(X) with no output arguments plots the PSD in the current
% figure window, with confidence intervals.
%
% The default values for the parameters are NFFT = 256 (or SIZE(X,1),
% whichever is smaller), NOVERLAP = 0, WINDOW = HANNING(NFFT), Fs = 2,
% and Pr = .95. You can obtain a default parameter by leaving it out
% or inserting an empty matrix [], e.g. SPECTRUM(X,[],128).
%
% P = SPECTRUM2(X,Y) performs spectral analysis of the two times SIZE(X,2)
% sequences X and Y using the Welch method. SPECTRUM returns the 8 times
% SIZE(X,2)column array
% P = [Pxx Pyy Pxy Txy Cxy Pxxc Pyyc Pxyc]
% where
% Pxx = X-vector power spectral density
% Pyy = Y-vector power spectral density
% Pxy = Cross spectral density
% Txy = Complex transfer function from X to Y = Pxy./Pxx
% Cxy = Coherence function between X and Y = (abs(Pxy).^2)./(Pxx.*Pyy)
% Pxxc,Pyyc,Pxyc = Confidence range.
% All input and output options are otherwise exactly the same as for the
% single input case.
%
% SPECTRUM2(X,Y) with no output arguments will plot Pxx, Pyy, abs(Txy),
% angle(Txy) and Cxy in sequence, pausing between plots.
%
% SPECTRUM2(X,...,DFLAG), where DFLAG can be 'linear', 'mean' or 'none',
% specifies a detrending mode for the prewindowed sections of X (and Y).
% DFLAG can take the place of any parameter in the parameter list
% (besides X) as long as it is last, e.g. SPECTRUM(X,'none');
%
% See also SPECTRUM, PSD, CSD, TFE, COHERE, SPECGRAM, SPECPLOT, DETREND,
% PMTM, PMUSIC.
% ETFE, SPA, and ARX in the Identification Toolbox.
% The units on the power spectra Pxx and Pyy are such that, using
% Parseval's theorem:
%
% SUM(Pxx)/LENGTH(Pxx) = SUM(X.^2)/size(x,1) = COV(X)
%
% The RMS value of the signal is the square root of this.
% If the input signal is in Volts as a function of time, then
% the units on Pxx are Volts^2*seconds = Volt^2/Hz.
%
% Here are the covariance, RMS, and spectral amplitude values of
% some common functions:
% Function Cov=SUM(Pxx)/LENGTH(Pxx) RMS Pxx
% a*sin(w*t) a^2/2 a/sqrt(2) a^2*LENGTH(Pxx)/4
%Normal: a*rand(t) a^2 a a^2
%Uniform: a*rand(t) a^2/12 a/sqrt(12) a^2/12
%
% For example, a pure sine wave with amplitude A has an RMS value
% of A/sqrt(2), so A = SQRT(2*SUM(Pxx)/LENGTH(Pxx)).
%
% See Page 556, A.V. Oppenheim and R.W. Schafer, Digital Signal
% Processing, Prentice-Hall, 1975.
error(nargchk(1,8,nargin))
[msg,x,y,nfft,noverlap,window,Fs,p,dflag]=specchk2(varargin);
error(msg)
if isempty(p),
p = .95; % default confidence interval even if not asked for
end
n = size(x,1); % Number of data points
ns = size(x,2); % Number of signals
nwind = length(window);
if n < nwind % zero-pad x (and y) if length less than the window length
x(nwind,:)=0; n=nwind;
if ~isempty(y), y(nwind)=0; end
end
k = fix((n-noverlap)/(nwind-noverlap)); % Number of windows
index = 1:nwind;
KMU = k*norm(window)^2; % Normalizing scale factor ==> asymptotically unbiased
% KMU = k*sum(window)^2;% alt. Nrmlzng scale factor ==> peaks are about right
if (isempty(y)) % Single sequence case.
Pxx = zeros(nfft,ns); Pxx2 = zeros(nfft,ns);
for i=1:k
for l=1:ns
if strcmp(dflag,'linear')
xw = window.*detrend(x(index,l));
elseif strcmp(dflag,'none')
xw = window.*(x(index,l));
else
xw = window.*detrend(x(index,l),0);
end
Xx = abs(fft(xw,nfft)).^2;
Pxx(:,l) = Pxx(:,l) + Xx;
Pxx2(:,l) = Pxx2(:,l) + abs(Xx).^2;
end
index = index + (nwind - noverlap);
end
% Select first half
if ~any(any(imag(x)~=0)), % if x and y are not complex
if rem(nfft,2), % nfft odd
select = [1:(nfft+1)/2];
else
select = [1:nfft/2+1]; % include DC AND Nyquist
end
else
select = 1:nfft;
end
Pxx = Pxx(select,:);
Pxx2 = Pxx2(select,:);
cPxx = zeros(size(Pxx));
if k > 1
c = (k.*Pxx2-abs(Pxx).^2)./(k-1);
c = max(c,zeros(size(Pxx)));
cPxx = sqrt(c);
end
ff = sqrt(2)*erfinv(p); % Equal-tails.
Pxxc = ff.*cPxx/KMU;
P = Pxx/KMU;
Pc = Pxxc;
else
Pxx = zeros(nfft,ns); % Dual sequence case.
Pxy = Pxx; Pxx2 = Pxx; Pxy2 = Pxx;
Pyy = zeros(nfft,1); Pyy2 = Pyy;
for i=1:k
if strcmp(dflag,'linear')
yw = window.*detrend(y(index));
elseif strcmp(dflag,'none')
yw = window.*(y(index));
else
yw = window.*detrend(y(index),0);
end
Yy = fft(yw,nfft);
Yy2 = abs(Yy).^2;
Pyy = Pyy + Yy2;
Pyy2 = Pyy2 + abs(Yy2).^2;
for l=1:ns
if strcmp(dflag,'linear')
xw = window.*detrend(x(index,l));
elseif strcmp(dflag,'none')
xw = window.*(x(index,l));
else
xw = window.*detrend(x(index,l),0);
end
Xx = fft(xw,nfft);
Xx2 = abs(Xx).^2;
Pxx(:,l) = Pxx(:,l) + Xx2;
Pxx2(:,l) = Pxx2(:,l) + abs(Xx2).^2;
Xy = Yy .* conj(Xx);
Pxy(:,l) = Pxy(:,l) + Xy;
Pxy2(:,l) = Pxy2(:,l) + Xy .* conj(Xy);
end
index = index + (nwind - noverlap);
end
% Select first half
if ~any(any(imag([x y])~=0)), % if x and y are not complex
if rem(nfft,2), % nfft odd
select = [1:(nfft+1)/2];
else
select = [1:nfft/2+1]; % include DC AND Nyquist
end
else
select = 1:nfft;
end
Pxx = Pxx(select,:);
Pxy = Pxy(select,:);
Pxx2 = Pxx2(select,:);
Pxy2 = Pxy2(select,:);
Pyy = Pyy(select);
Pyy2 = Pyy2(select);
cPxx = zeros(size(Pxx));
cPyy = zeros(size(Pyy));
cPxy = cPxx;
if k > 1
c = max((k.*Pxx2-abs(Pxx).^2)./(k-1),zeros(size(Pxx)));
cPxx = sqrt(c);
c = max((k.*Pyy2-abs(Pyy).^2)./(k-1),zeros(size(Pyy)));
cPyy = sqrt(c);
c = max((k.*Pxy2-abs(Pxy).^2)./(k-1),zeros(size(Pxx)));
cPxy = sqrt(c);
end
Txy = Pxy./Pxx;
Cxy = (abs(Pxy).^2)./(Pxx.*repmat(Pyy,1,size(Pxx,2)));
ff = sqrt(2)*erfinv(p); % Equal-tails.
Pxx = Pxx/KMU;
Pyy = Pyy/KMU;
Pxy = Pxy/KMU;
Pxxc = ff.*cPxx/KMU;
Pxyc = ff.*cPxy/KMU;
Pyyc = ff.*cPyy/KMU;
P = [Pxx Pyy Pxy Txy Cxy];
Pc = [Pxxc Pyyc Pxyc];
end
freq_vector = (select - 1)'*Fs/nfft;
if nargout == 0, % do plots
newplot;
if Fs==2, xl='Frequency'; else, xl = 'f [Hz]'; end
nplot=1+(1-isempty(y))*4;
subplot(nplot,1,1);
c = [max(Pxx-Pxxc,0) Pxx+Pxxc];
c = c.*(c>0);
h=semilogy(freq_vector,Pxx,...
freq_vector,c(:,1:size(c,2)/2),'--',...
freq_vector,c(:,size(c,2)/2+1:end),'--');
title('\bf X Power Spectral Density')
ylabel('P_x')
xlabel(xl)
if length(h)>3
s={};
for k=1:length(h)/3
c=get(h(k),'Color');
set(h(k+length(h)/3),'Color',c);
set(h(k+2*length(h)/3),'Color',c);
s{k}=['x_' num2str(k)];
end
legend(h(1:length(h)/3),s);
end
if (isempty(y)), % single sequence case
return
end
subplot(nplot,1,2);
c = [max(Pyy-Pyyc,0) Pyy+Pyyc];
c = c.*(c>0);
h=semilogy(freq_vector,Pyy,...
freq_vector,c(:,1),'--',...
freq_vector,c(:,2),'--');
if size(Pxx,2)>1
for k=1:length(h)/3
c=get(h(k),'Color');
set(h(k+length(h)/3),'Color',c);
set(h(k+2*length(h)/3),'Color',c);
end
end
title('\bf Y Power Spectral Density')
ylabel('P_y')
xlabel(xl)
subplot(nplot,1,3);
semilogy(freq_vector,abs(Txy));
title('\bf Transfer function magnitude')
ylabel('T_{xy}^{(m)}')
xlabel(xl)
subplot(nplot,1,4);
plot(freq_vector,(angle(Txy))), ...
title('\bf Transfer function phase')
ylabel('T_{xy}^{(p)}')
xlabel(xl)
subplot(nplot,1,5);
plot(freq_vector,Cxy);
title('\bf Coherence')
ylabel('C_{xy}')
xlabel(xl)
if exist ('niceaxes') ~= 0
niceaxes(findall(gcf,'Type','axes'));
end
elseif nargout ==1,
Spec = P;
elseif nargout ==2,
Spec = P;
f = freq_vector;
elseif nargout ==3,
Spec = P;
f = freq_vector;
SpecConf = Pc;
end
function [msg,x,y,nfft,noverlap,window,Fs,p,dflag] = specchk2(P)
%SPECCHK Helper function for SPECTRUM
% SPECCHK(P) takes the cell array P and uses each cell as
% an input argument. Assumes P has between 1 and 7 elements.
msg = [];
if size(P{1},1)<=1
if max(size(P{1}))==1
msg = 'Input data must be a vector, not a scalar.';
else
msg = 'Requires column vector input.';
end
x=[];
y=[];
elseif (length(P)>1),
if (all(size(P{1},1)==size(P{2})) & (size(P{1},1)>1) ) | ...
size(P{2},1)>1, % 0ne signal or 2 present?
% two signals, x and y, present
x = P{1}; y = P{2};
% shift parameters one left
P(1) = [];
else
% only one signal, x, present
x = P{1}; y = [];
end
else % length(P) == 1
% only one signal, x, present
x = P{1}; y = [];
end
% now x and y are defined; let's get the rest
if length(P) == 1
nfft = min(size(x,1),256);
window = hanning(nfft);
noverlap = 0;
Fs = 2;
p = [];
dflag = 'linear';
elseif length(P) == 2
if isempty(P{2}), dflag = 'linear'; nfft = min(size(x,1),256);
elseif isstr(P{2}), dflag = P{2}; nfft = min(size(x,1),256);
else dflag = 'linear'; nfft = P{2}; end
window = hanning(nfft);
noverlap = 0;
Fs = 2;
p = [];
elseif length(P) == 3
if isempty(P{2}), nfft = min(size(x,1),256); else nfft=P{2}; end
if isempty(P{3}), dflag = 'linear'; noverlap = 0;
elseif isstr(P{3}), dflag = P{3}; noverlap = 0;
else dflag = 'linear'; noverlap = P{3}; end
window = hanning(nfft);
Fs = 2;
p = [];
elseif length(P) == 4
if isempty(P{2}), nfft = min(size(x,1),256); else nfft=P{2}; end
if isstr(P{4})
dflag = P{4};
window = hanning(nfft);
else
dflag = 'linear';
window = P{4}; window = window(:); % force window to be a column
if length(window) == 1, window = hanning(window); end
if isempty(window), window = hanning(nfft); end
end
if isempty(P{3}), noverlap = 0; else noverlap=P{3}; end
Fs = 2;
p = [];
elseif length(P) == 5
if isempty(P{2}), nfft = min(size(x,1),256); else nfft=P{2}; end
window = P{4}; window = window(:); % force window to be a column
if length(window) == 1, window = hanning(window); end
if isempty(window), window = hanning(nfft); end
if isempty(P{3}), noverlap = 0; else noverlap=P{3}; end
if isstr(P{5})
dflag = P{5};
Fs = 2;
else
dflag = 'linear';
if isempty(P{5}), Fs = 2; else Fs = P{5}; end
end
p = [];
elseif length(P) == 6
if isempty(P{2}), nfft = min(size(x,1),256); else nfft=P{2}; end
window = P{4}; window = window(:); % force window to be a column
if length(window) == 1, window = hanning(window); end
if isempty(window), window = hanning(nfft); end
if isempty(P{3}), noverlap = 0; else noverlap=P{3}; end
if isempty(P{5}), Fs = 2; else Fs = P{5}; end
if isstr(P{6})
dflag = P{6};
p = [];
else
dflag = 'linear';
if isempty(P{6}), p = .95; else p = P{6}; end
end
elseif length(P) == 7
if isempty(P{2}), nfft = min(size(x,1),256); else nfft=P{2}; end
window = P{4}; window = window(:); % force window to be a column
if length(window) == 1, window = hanning(window); end
if isempty(window), window = hanning(nfft); end
if isempty(P{3}), noverlap = 0; else noverlap=P{3}; end
if isempty(P{5}), Fs = 2; else Fs = P{5}; end
if isempty(P{6}), p = .95; else p = P{6}; end
if isstr(P{7})
dflag = P{7};
else
msg = 'DFLAG parameter must be a string.'; return
end
end
% NOW do error checking
if isempty(msg)
if (nfft<length(window)),
msg = 'Requires window''s length to be no greater than the FFT length.';
end
if (noverlap >= length(window)),
msg = 'Requires NOVERLAP to be strictly less than the window length.';
end
if (nfft ~= abs(round(nfft)))|(noverlap ~= abs(round(noverlap))),
msg = 'Requires positive integer values for NFFT and NOVERLAP.';
end
if ~isempty(p),
if (prod(size(p))>1)|(p(1,1)>1)|(p(1,1)<0),
msg = 'Requires confidence parameter to be a scalar between 0 and 1.';
end
end
if (min(size(y))~=1)&(~isempty(y)),
msg = 'Requires column vector input as second signal.';
end
if (size(x,1)~=length(y))&(~isempty(y)),
msg = 'Requires X and Y to have the same number of rows.';
end
end

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