how to recalibrate two curves in time? - matlab

Question

I am currently processing EMG signals obtained on a bicep curl exercise under different conditions. At the end of my code I replace the normalized signals of each condition and that as a function of time. my problem is that during this superposition peaks puffs are shifted in time from one curve to another because the participants did not start at the same time its exercise and I'd like to "recalibrate" (I do not I'm not sure this is the right word of the shot) the curves in time for each contraction to start and finish at the same time (on the blue curve there is a contraction of more at the end)
this is what my code looks like for now
%% Process EMG dynamique
clc, clear all, close all
%% Haltère 10 Kg
%% Filtrage, centrage et rectication du signal
data_EMG = load([''10kg_haltere-Philippe.txt'']); % Load file EMG
fe_EMG = 1000; % sampling frequency Acceleration Hz
timeEMG_10 = (0:1/fe_EMG:(length(data_EMG)-1)*(1/fe_EMG))'; % Time vector
for m = 1 : 2
[B,A] = butter(8/2,[15*1.247 400*1.247]/(fe_EMG/2),'bandpass'); % filter butterworth band pass 20 à 400 Hz d'ordre 4
data_EMG_filt = filtfilt(B,A,data_EMG(:,m)); % filtring pass band
data_EMG_filt_1 = data_EMG_filt - ones(length(data_EMG_filt),1)*mean(data_EMG_filt); %Centering of the EMG signal around the individual mean of each muscle
data_EMG_filt_rectified = abs(data_EMG_filt_1); % Rectification of the EMG signal = Full wave rectification
%% courbe RMS/EMG
rms_window = 1300;
for i = (rms_window/2)+1 : length(data_EMG)-(rms_window/2)
rms_data_EMG(i) = rms(data_EMG_filt_rectified([i-(rms_window/2):i+(rms_window/2)]));
end
[B,A] = butter(4/2,[5*1.247]/(fe_EMG/2),'low'); % filter butterworth band pass 20 à 400 Hz d'ordre 4
data_EMG_filt_rectified_filtbutter = filtfilt(B,A,data_EMG_filt_rectified); % filtring pass band
EMG_max = max(data_EMG_filt_rectified_filtbutter);
data_EMG_filt_rectified_filtbutter_norm_10 = (data_EMG_filt_rectified_filtbutter.*100)./EMG_max;
% Stockage
RMS(:,m) = rms_data_EMG;
EMG_filt(:,m) = data_EMG_filt_rectified;
EMG_filtbutter(:,m) = data_EMG_filt_rectified_filtbutter;
EMG_filtbutter_norm(:,m) = data_EMG_filt_rectified_filtbutter_norm_10;
end
%% Haltère 5 kg
%% Filtrage, centrage et rectication du signal
data_EMG = load(['5kg_haltere-Philippe.txt']); % Load file EMG
fe_EMG = 1000; % sampling frequency Acceleration Hz
timeEMG_5 = (0:1/fe_EMG:(length(data_EMG)-1)*(1/fe_EMG))'; % Time vector
for m = 1 : 2
[B,A] = butter(4/2,[15*1.247 400*1.247]/(fe_EMG/2),'bandpass'); % filter butterworth band pass 20 à 400 Hz d'ordre 4
data_EMG_filt = filtfilt(B,A,data_EMG(:,m)); % filtring pass band
data_EMG_filt_1 = data_EMG_filt - ones(length(data_EMG_filt),1)*mean(data_EMG_filt); %Centering of the EMG signal around the individual mean of each muscle
data_EMG_filt_rectified = abs(data_EMG_filt_1); % Rectification of the EMG signal = Full wave rectification
%% courbe RMS/EMG
rms_window = 1300;
for i = (rms_window/2)+1 : length(data_EMG)-(rms_window/2)
rms_data_EMG(i) = rms(data_EMG_filt_rectified([i-(rms_window/2):i+(rms_window/2)]));
end
% Application d'un deuxième filtre (pour analyser les bouffé EMG) à la place de lp filter
[B,A] = butter(8/2,[5*1.247]/(fe_EMG/2),'low');
data_EMG_filt_rectified_filtbutter = filtfilt(B,A,data_EMG_filt_rectified);
EMG_max = max(data_EMG_filt_rectified_filtbutter);
data_EMG_filt_rectified_filtbutter_norm_5 = (data_EMG_filt_rectified_filtbutter.*100)./EMG_max;
% Stockage
RMS(:,m) = rms_data_EMG;
EMG_filt(:,m) = data_EMG_filt_rectified;
EMG_filtbutter(:,m) = data_EMG_filt_rectified_filtbutter;
EMG_filtbutter_norm_5(:,m) = data_EMG_filt_rectified_filtbutter_norm_5;
end
figure
plot(timeEMG_10,EMG_filtbutter_norm(:,1))
hold on
plot(timeEMG_5,data_EMG_filt_rectified_filtbutter_norm_5)
hold off
Link to data

Answer 1

I made up my own function for something similar. I am sure there are probably better ways to do this however it works most of the time. The basic ideas is to shift one of the lines 1 point at a time (limited to some +/- range) and check the RMSE between the 2. Record where the lowest RMSE occurs and that is how far you should shift.
Time aligning function:
function [time2] = dataSync(data1, data2, time2, maxShift)
minError = inf;
shiftPoint = NaN;
for ii = -maxShift:maxShift
if ii <= 0 %Shift data 2 to the left
RMSE = sqrt(mean((data1(1:end+ii) - data2(1-ii:end)).^2));
else %Shift data 2 to the right (...or data 1 left)
RMSE = sqrt(mean((data1(1+ii:end) - data2(1:end-ii)).^2));
end
if RMSE < minError
minError = RMSE;
shiftPoint = ii;
end
end
if shiftPoint ~= 0
time2 = time2 + time2(abs(shiftPoint))*sign(shiftPoint);
end
Putting it in your code:
Note that I limited the shift to +/- 5000 samples.
figure
plot(timeEMG_10,EMG_filtbutter_norm(:,1))
hold on
%% Try to line up the times.
[timeSync] = dataSync(EMG_filtbutter_norm(:,1), data_EMG_filt_rectified_filtbutter_norm_5, timeEMG_5, 5000);
% plot(timeEMG_5,data_EMG_filt_rectified_filtbutter_norm_5)
% hold off
plot(timeSync,data_EMG_filt_rectified_filtbutter_norm_5,'g')
hold off
Gives a lined up plot that
Used to be:
And now is:
Note that you don't have the same number of peaks but that is probably the best that you can do. Also there is the assumption that the 2 data arrays have the same number of elements, same original time vectors, etc. which might not always be true.