Fitting real data curve to a homogeneous diff

Hello! I measured accelerations with matlab Mobile and I encountered the problem that the time step was not homogeneous and therefore the measured frequency. Therefore, I created a homogeneous diff (blue curve) and I would like to find a code in MATLAB that adapts the measured function with the real values (red curve) to that homogeneous time increment.

I attach a picture of the problem.

Answer 1

[Star Strider]

I am not certain from your description what you want to do. However if you have the Signal Processing Toolbox, the resample function coukld be appropriate. (It is preferable to interp1 for singal processing applications.)

[Daniel Sánchez Muñoz]

Hello! Thanks for the reply.

There is the red curve with the real values, and the blue curve with an homogeneous timestamp (created from the red curve). I want the blue curve to be as similar as possible to the red curve.

Do you know any interpolation function that is very very accurate?

Thanks

[Star Strider]

Without having the data to work with, I cannot add anything to what I wrote earlier.

[Daniel Sánchez Muñoz]

The code is below. What it does is to homogenize the time step, and it uses an interp1. I don't have the file, but it consists of a column with the time in seconds and a column with the acceleration measurements.

FICHERO = '2019-02-12-01-24-51-FRacels.csv'; COLTIME = 1; COLACEL = 1; fs = 100;

data = load(FICHERO); t = (data(:, COLTIME) - data(1, COLTIME)) / 1000; v = data(:, 2:end);

% Interpolate data to assure constant time interval at fs dt = 1 / fs; tq = zeros(1,length(data)); for i = 2:length(data) tq(i) = tq(i-1) + dt; end

vq = interp1(t, v(:,COLACEL), tq,'spline','extrap'); %vq = makima(t, v(:,COLACEL), tq); %'linear'); %'nearest'); %'pchip'); %'cubic'); %'makima'); %'spline');

% Reconstruct the data vector data = [tq', vq'];

% Plot original data and interpolated data line figure plot(t, v(:,COLACEL), 'xr-') hold on plot(tq, vq, 'ob-'); legend('Samples', 'Spline Interpolation') xlim([t(1) t(end)]) title('Original and interpolated data')

figure plot(diff(t),'xr') hold on plot(diff(tq),'ob-') legend('Samples', 'Spline Interpolation')

[Star Strider]

Without having the data to work with, I cannot add anything to what I wrote earlier.

[Daniel Sánchez Muñoz]

I attach the full code and the file with the acceleration measurements.

But the "Timestamp correction" don't work.

[Star Strider]

I am not certain what result you want.

This resamples all of them to a common sampling frequency. There are some obvious differences between the original and resampled signals.

The resample function has a number of options, including the interplation method (I chose the default 'linear' method for all of these). You can slso choose a different sampling frequency (I chose 10 Hz here because it is closest to the actual sampling frequency), although that may create data where no data previously existed, so I advise against it.

LD = load('Prueba.mat')

LD = struct with fields:
    Acceleration: [53×3 timetable]

Acceleration = LD.Acceleration

Acceleration = 53×3 timetable
           Timestamp                X           Y          Z   
    ________________________    _________    ________    ______

    03-May-2023 10:44:45.299      0.13878     0.22851    9.7723
    03-May-2023 10:44:45.399      0.11067     0.26082    9.7846
    03-May-2023 10:44:45.499      0.14267     0.25065    9.9921
    03-May-2023 10:44:45.599      0.10857       0.367     9.551
    03-May-2023 10:44:45.699     0.085244     0.41575    9.9479
    03-May-2023 10:44:45.799     0.034098     0.23659    10.891
    03-May-2023 10:44:45.899      0.14656     0.18036    9.5495
    03-May-2023 10:44:45.999      0.16839       0.533    9.5333
    03-May-2023 10:44:46.099    -0.085244     0.54646    10.048
    03-May-2023 10:44:46.199     -0.11396     0.70947    9.1247
    03-May-2023 10:44:46.299      0.20489      1.0379    7.2703
    03-May-2023 10:44:46.399     0.068495     0.15165    8.4736
    03-May-2023 10:44:46.499     -0.27159    -0.26889     13.35
    03-May-2023 10:44:46.599      0.24796    -0.33918    12.625
    03-May-2023 10:44:46.699     -0.49741     0.40229    9.0996
    03-May-2023 10:44:46.799     0.046361     0.84347     6.553

VN = Acceleration.Properties.VariableNames;

[h,m,s] = hms(Acceleration.Timestamp);
s

s = 53×1

45.2990 45.3990 45.4990 45.5990 45.6990 45.7990 45.8990 45.9990 46.0990 46.1990

% X = Acceleration.X
% Y = Acceleration.Y
% Z = Acceleration.Z

format long
ds = diff(s);
ds_stats = [min(ds); max(ds); mean(ds); std(ds); 1/mean(ds)]        % 'Original' Time Vector Statistics

ds_stats = 5×1

0.099999999999994 0.100999999999999 0.100019230769231 0.000138675049056 9.998077292828301

Fs = ds_stats(end)

Fs = 
   9.998077292828301

Fsc = ceil(Fs)

Fsc = 
    10

Accelerationr = resample(Acceleration, Fsc)                         % 'Accelerationr' Is The Resampled 'Acceleration' 'timetable'

Accelerationr = 53×3 timetable
              Time                  X            Y            Z    
    ________________________    _________    _________    _________

    03-May-2023 10:44:45.299     0.138784     0.228515     9.772287
    03-May-2023 10:44:45.399     0.110668     0.260818     9.784551
    03-May-2023 10:44:45.499     0.142672     0.250648     9.992128
    03-May-2023 10:44:45.599     0.108574     0.366999     9.550952
    03-May-2023 10:44:45.699     0.085244     0.415753     9.947861
    03-May-2023 10:44:45.799     0.034098      0.23659    10.891232
    03-May-2023 10:44:45.899      0.14656     0.180359     9.549456
    03-May-2023 10:44:45.999     0.168395     0.533001     9.533304
    03-May-2023 10:44:46.099    -0.085244     0.546461     10.04836
    03-May-2023 10:44:46.199    -0.113958     0.709472      9.12473
    03-May-2023 10:44:46.299     0.204885     1.037887     7.270292
    03-May-2023 10:44:46.399     0.068495     0.151645     8.473583
    03-May-2023 10:44:46.499    -0.271585    -0.268893    13.349558
    03-May-2023 10:44:46.599     0.247956    -0.339183    12.625429
    03-May-2023 10:44:46.699    -0.497408     0.402293     9.099606
    03-May-2023 10:44:46.799     0.046361      0.84347     6.553044

[h,m,s] = hms(Accelerationr.Time);
ds = diff(s);
ds_stats = [min(ds); max(ds); mean(ds); std(ds); 1/mean(ds)]        % 'Resampled' Time Vector Statistics

ds_stats = 5×1

0.099999999999994 0.100000000000001 0.100000000000000 0.000000000000003 9.999999999999995

figure
tiledlayout(3,1)
for k = 1:3
    nexttile
    plot(Acceleration.Timestamp, Acceleration{:,k})
    title(VN{k})
    grid
    ylim('padded')
end
sgtitle('Original')

figure
tiledlayout(3,1)
for k = 1:3
    nexttile
    plot(Accelerationr.Time, Accelerationr{:,k})
    grid
    title(VN{k})
    ylim('padded')
end
sgtitle('Resampled')

figure
tiledlayout(3,1)
for k = 1:3
    nexttile
    plot(Acceleration.Timestamp, Acceleration{:,k}, 'DisplayName','Original')
    hold on
    plot(Accelerationr.Time, Accelerationr{:,k}, 'DisplayName','Resampled')
    hold off
    grid
    title(VN{k})
    if k == 1
    legend('Location','best')
    end
    ylim('padded')
end
sgtitle('Original Co-Plotted With Resampled')

figure
k = 2;
plot(Acceleration.Timestamp, Acceleration{:,k}, 'DisplayName','Original')
hold on
plot(Accelerationr.Time, Accelerationr{:,k}, 'DisplayName','Resampled')
hold off
grid
title(VN{k})
legend('Location','best')

I am not certain what part of what signal is in the originally provided plot image, or I would post it in detail here.

.

[Daniel Sánchez Muñoz]

Hello!

Thanks for your help. The problem is that you use the mean frecuency, so there is still a non homogeneus sample frecuency.

I have finally solved the problem.

Pd.: Do I have to accept your answer? I thank you very much for the help.

data=[t,z];
COLTIME = 1;
COLACEL = 1;
tt = (data(:, COLTIME) - data(1, COLTIME)); 
v = data(:, 2:end);
    % Interpolate data to assure constant time interval at fs:
dt = 1 / fs;

ntime = length(data);
tq = zeros(1,ntime);
for i = 2:ntime
    tq(i) = tq(i-1) + dt;
end
vq = interp1(tt, v(:,COLACEL), tq,'spline','extrap');
    % Reconstruct the data vector:
data = [tq', vq'];

[Star Strider]

I would appreciate it if you would accept my answer.

I actually use the most common frequency, that I derive from the differences in the sampling intervals. I use mean, I also could have used mode.

I notice the the code you posted uses ‘fs’ to define ‘dt’ without first defining ‘fs’. I have no idea how you define ‘fs’.

I also use resample instead of interp1 because resample uses an anti-aliasing filter. This is important for signal processing applications, and signal processing is apprarently what you want to do.

The resample function also has the 'spline' option as an interpolation method. I rarely use it (preferring 'pchip') because it can give some wildly varying results.

.