Flatten plot from two vectors

There are two data vectors. when plotting I get a sawtooth, would I like to smooth the graph?

How to do this?

Thank you in advance!

Answer 1

[Mathieu NOE]

hello

a small demo to compare smoothing and spline fitting (using this FEX submission : SPLINEFIT - File Exchange - MATLAB Central (mathworks.com))

n = 25;
x = sort(4*rand(n,1))
f = sin(x) + 0.05*randn(n,1);

% resample the data (interpolation) on linearly spaced points
xx = linspace(min(x),max(x),100);
ff = interp1(x,f,xx);

% smoothing
ffs = smoothdata(ff, 'gaussian',10);

% or spline fit ? 
% Breaks interpolated from data 
breaks = linspace(min(x),max(x),10); % 
p = splinefit(xx,ff,breaks);  % 
ff2 = ppval(p,xx);

figure(1),
plot(x,f,'-*',xx,ffs,'-',xx,ff2,'-')
legend('raw','smoothed','spline fit');

[Lev Mihailov]

@Mathieu NOE The code gives an error

Error using matlab.internal.math.interp1
Sample points must be unique.

Error in interp1 (line 188)
        VqLite = matlab.internal.math.interp1(X,V,method,method,Xqcol);

Error in untitled (line 47)
ff = interp1(x,y,xx);

I have attached the dataset

[Mathieu NOE]

hello Lev

I have added these two lines to make sure your data has no duplicates , which is the reason why you get the error

[x,ia,ic] = unique(x);
y = y(ia);

full code

clearvars
clc


A=load('DataBetaGama.csv');
x = A(:,1);
y = A(:,2);
[x,ia,ic] = unique(x);
y = y(ia);


% resample the data (interpolation) on linearly spaced points
xx = linspace(min(x),max(x),100);
yy = interp1(x,y,xx);

% smoothing
yys = smoothdata(yy, 'gaussian',10);

% or spline fit ? 
% Breaks interpolated from data 
breaks = linspace(min(x),max(x),10); % 
p = splinefit(xx,yy,breaks);  % 
yy2 = ppval(p,xx);

figure(1),
plot(x,y,'-*',xx,yys,'-',xx,yy2,'-')
legend('raw','smoothed','spline fit');

same comment as @William Rose, the data set is not what I expected , it's already very smmoth - not the staircase plot you mentionned in first place. can you double check you sent the right data file ?

[Lev Mihailov]

@Mathieu NOE This is my data, ladder plot appears as the graph approaches. Graph should be smooth.

[Mathieu NOE]

ok , I didn't notice that in first place . You need a lot of zoom to see the staircase

with smoothdata you can get the desired result

clearvars
clc

A=load('DataBetaGama.csv');
x = A(:,1);
y = A(:,2);
[x,ia,ic] = unique(x);
samples = numel(x);

y = y(ia);
plot(x,y,'-r');

% resample the data (interpolation) on linearly spaced points
xx = linspace(min(x),max(x),2*samples);
yy = interp1(x,y,xx);

% smoothing
win = round(samples/25);
yys = smoothdata(yy, 'gaussian',win);

figure(1),
plot(x,y,'-*',xx,yys)
legend('raw','smoothed');

Answer 2

[William Rose]

@Lev Mihailov,

Can you attach the vectors please?

I cannot tell from the plot if the samlpling is uniform along x or not. I cannot tell if this is a path in two dimensions, or a function of the horizontal axis variable. Thie difference matters, because the approach to smoothing will be different.

If it is a path in 2 dimensions, with non-uniform sampling along x and along y:

Conisder defining an arbitray time variable, so that x and y both become funcitons of time. I would assign times to each point pair so that the distance travelled per unit time (where ) is constant. Use interp1() to resample the x-vector to uniform spacing in time. Do the same with the y vector. Choose a time spacing that is sufficiently fine to accurately capture the sharp corners in your data. The plot of resampled x versus resampled y should look like the original.

Then apply a flat moving average filter to the x versus time data and to the y versus time data, independently. Experiment with different widths for the moving average window. Think about how to handle the moving average window when it gets up to the edges of the signal.

If, instead of being a path in two dimensions, this is a plot of a dependent variable (y) versus an independent variable (x), then smooth the y values, and don't smooth the x values. If x-values are non-uniformly spaced, then interpolate the y values to to a uniform sampling rate along the x axis, using interp1(). Make sure the sampling interval along x is dense enough to capture accurately the sharp corners in the original data. Then smooth the interpolated y values with a flat moving average filter. Try different window widths. As usual, take care with the moving average near the edges.

[William Rose]

@Lev Mihailov, in case you are not familiar with a moving average window, here is an example of one way to do it:

N=100;
y=rand(1,N);
x=1:N;
M=7;  %window width (should be odd)
for i=(M+1)/2:N-(M-1)/2
    y7(i-(M-1)/2)=sum(y(i-(M-1)/2:i+(M-1)/2))/M;
end
x7=(M+1)/2:N-(M-1)/2;
plot(x,y,'-r.',x7,y7,'-b.');
xlabel('X'); ylabel('Y'); legend('Raw','Smoothed'); grid on;

Try it.

[Lev Mihailov]

@William Rose I've attached vectors, vertical and horizontal data are being captured by the sensor.

[William Rose]

@Lev Mihailov,

The data file you attached when plotted generates the plot below, which is very different from the plot in the original post. This data already looks very smooth at this scale.

A=load('DataBetaGama.csv');
plot(A(:,1),A(:,2),'-r');

Is this the data you want to smooth?

[Lev Mihailov]

@William Rose Yes, this data, with a large approximation, you can see the steps (saws) that I want to smooth out