Can I remove the noise and make the graph smooth?

I drew a graph with data obtained in seconds when my feet touch the ground while walking. By the way, the graph is not smooth, so I want to make it smooth. I don't know if I should remove noise, filter it, or how to do it. Please help me!!

This is my code, and when I run it like this, I get some of the following graphs.

Fz = -temp1(7000:8600,5)%%%data%%%

for i=1:length(Fz)

plot(Fz,'b')

hold on

plot(i,Fz(i))

line([800 i], [0 Fz(i)])

pause(0.005)

end

[Adam Danz]

It would be helpful to define "noise" in your example. Do you expect the eliminate the incline from the oscillations (as in Mathiue NOE's helpful answer) or do you expect to eliminate the oscillations to reveal a curve that slowly inclines?

[JooYoung Jeon]

The graph of the original post is part of the graph I drew. The overall form is similar to what I posted in the comments now, but the graph I drew vibrates a lot. So, I want to draw a smooth graph similar to the graph posted in the comments.

[Adam Danz]

Look into these options

• spline
• smooth

[JooYoung Jeon]

How should I apply the code I wrote to the smooth code?

This picture is a plot written in the code below. I want to make it smooth.

Fz = -temp1(7000:8600,5)%%%data%%%

for i=1:length(Fz)

plot(Fz,'b')

hold on

plot(i,Fz(i))

line([800 i], [0 Fz(i)])

pause(0.00005)

end

Answer 1

[Mathieu NOE]

hello

see the demo below - it removes the drift in your data , so it will remain "zero mean" after high pass filtering

as a bonus I added some code to compute the time intervals define by threshold crossing

period = 0.8987 0.8972 0.8984 0.8980 0.8977 0.8963 (in seconds)

clc
clearvars

n=100;
x=linspace(0,2*pi,n);
y = sin(7*x)+0.1*x.^2;

% high pass filtered signal
[b,a] = butter(2,0.1,'high');
yf = filtfilt(b,a,y);

threshold = 0.25; % your value here

[t0_pos,s0_pos,t0_neg,s0_neg]= crossing_V7(yf,x,threshold,'linear'); % positive (pos) and negative (neg) slope crossing points 
% ind => time index (samples)
% t0 => corresponding time (x) values 
% s0 => corresponding function (y) values , obviously they must be equal to "threshold"

figure(1)
plot(x,y,x,yf,x,threshold*ones(size(x)),'k--',t0_pos,s0_pos,'dr',t0_neg,s0_neg,'dg','linewidth',2,'markersize',12);grid on
legend('signal','signal after HP filter','threshold','positive slope crossing points','negative slope crossing points');

period = diff(t0_pos)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t0_pos,s0_pos,t0_neg,s0_neg] = crossing_V7(S,t,level,imeth)

% [ind,t0,s0,t0close,s0close] = crossing_V6(S,t,level,imeth,slope_sign) % older format

% CROSSING find the crossings of a given level of a signal
%   ind = CROSSING(S) returns an index vector ind, the signal
%   S crosses zero at ind or at between ind and ind+1
%   [ind,t0] = CROSSING(S,t) additionally returns a time
%   vector t0 of the zero crossings of the signal S. The crossing
%   times are linearly interpolated between the given times t
%   [ind,t0] = CROSSING(S,t,level) returns the crossings of the
%   given level instead of the zero crossings
%   ind = CROSSING(S,[],level) as above but without time interpolation
%   [ind,t0] = CROSSING(S,t,level,par) allows additional parameters
%   par = {'none'|'linear'}.
%	With interpolation turned off (par = 'none') this function always
%	returns the value left of the zero (the data point thats nearest
%   to the zero AND smaller than the zero crossing).
%


% check the number of input arguments
error(nargchk(1,4,nargin));

% check the time vector input for consistency
if nargin < 2 | isempty(t)
	% if no time vector is given, use the index vector as time
    t = 1:length(S);
elseif length(t) ~= length(S)
	% if S and t are not of the same length, throw an error
    error('t and S must be of identical length!');    
end

% check the level input
if nargin < 3
	% set standard value 0, if level is not given
    level = 0;
end

% check interpolation method input
if nargin < 4
    imeth = 'linear';
end


% make row vectors
t = t(:)';
S = S(:)';

% always search for zeros. So if we want the crossing of 
% any other threshold value "level", we subtract it from
% the values and search for zeros.
S   = S - level;

% first look for exact zeros
ind0 = find( S == 0 ); 

% then look for zero crossings between data points
S1 = S(1:end-1) .* S(2:end);
ind1 = find( S1 < 0 );

% bring exact zeros and "in-between" zeros together 
ind = sort([ind0 ind1]);

% and pick the associated time values
t0 = t(ind); 
s0 = S(ind);

if ~isempty(ind)

    if strcmp(imeth,'linear')
        % linear interpolation of crossing
        for ii=1:length(t0)
            %if abs(S(ind(ii))) >= eps(S(ind(ii)))    % MATLAB V7 et +
            if abs(S(ind(ii))) >= eps*abs(S(ind(ii)))    % MATLAB V6 et -    EPS * ABS(X)

                % interpolate only when data point is not already zero
                NUM = (t(ind(ii)+1) - t(ind(ii)));
                DEN = (S(ind(ii)+1) - S(ind(ii)));
                slope =  NUM / DEN;
                slope_sign(ii) = sign(slope);
                t0(ii) = t0(ii) - S(ind(ii)) * slope;
                s0(ii) = level;
            end
        end
    end

    % extract the positive slope crossing points 
    ind_pos = find(sign(slope_sign)>0);
    t0_pos = t0(ind_pos);
    s0_pos = s0(ind_pos);

    % extract the negative slope crossing points 
    ind_neg = find(sign(slope_sign)<0);
    t0_neg = t0(ind_neg);
    s0_neg = s0(ind_neg);

else

    % empty output
    ind_pos = [];
    t0_pos = [];
    s0_pos = [];

    % extract the negative slope crossing points 
    ind_neg = [];
    t0_neg = [];
    s0_neg = [];
    
end

end

[JooYoung Jeon]

The graph of the original post is part of the graph I drew. The overall form is similar to what I posted in the comments now, but the graph I drew vibrates a lot. So, I want to draw a smooth graph similar to the graph posted in the comments.

[Mathieu NOE]

hello

ok, now I understand better - could you share the data ?

[JooYoung Jeon]

Here is data.

This picture is a plot written in the code below. I want to make it smooth.

Fz = -temp1(7000:8600,5)%%%data%%%

for i=1:length(Fz)

plot(Fz,'b')

hold on

plot(i,Fz(i))

line([800 i], [0 Fz(i)])

pause(0.00005)

end

[Mathieu NOE]

hello

this is it

I used smoothdata to denoise the data - but there are other options available , like smoothn (from File exchange)

clc
clearvars

T = readtable('KAS01_forceplate.xlsx');
[samples,col] = size(T);
x = (0:samples-1);
y = -T.Var5;
ind = 7000:8600;
x = x(ind);
y = y(ind);

ys = smoothdata(y,'gaussian',150);

plot(x,y,x,ys)
legend('raw','smoothed')

[JooYoung Jeon]

Thank you so much!!

By the way, can we draw a vertical line that goes up along the graph on the X-axis like a red line in that plot?

[Walter Roberson]

If you need the arrows, then either use annotation() or else use one of the arrow contributions from the File Exchange.. annotation() has some drawbacks because of its coordinate system.

If you do not need the arrows, then just draw a bunch of lines with plot() . If they all have the same color you can combine them, such as

x = [7075 7075 nan 7200 7200 nan 7375 7375 nan 7475 7475 nan 7675 7675 nan 7850 7850 nan 8075 8075 nan 8300 8300];
y = [   0  300 nan    0  475 nan    0  700 nan    0  700 nan    0   AND SO ON  ]
plot(x, y)

nan means to stop drawing the line and resume at the next pair of finite coordinates, so you can use this to create the appearance of multiple line segments.

[JooYoung Jeon]

You don't need an arrow. Can't you express it in the FOR-END phrase?

[JooYoung Jeon]

I want to go positive along the X-axis and make the line go up in real time.

[JooYoung Jeon]

Like this. in real time.

[Mathieu NOE]

hello

this will add the vertical lines one after one with a delay of 0.5 s

clc
clearvars
close all

T = readtable('KAS01_forceplate.xlsx');
[samples,col] = size(T);
x = (0:samples-1);
y = -T.Var5;
ind = 7000:8600;
x = x(ind);
y = y(ind);

ys = smoothdata(y,'gaussian',150);

figure(1)
plot(x,y,x,ys)
hold on

% adding vertical lines 
n = 20; % number of lines
xx=linspace(x(1),x(end),n);
yy = interp1(x,ys,xx);

for ci=1:n
        plot([xx(ci) xx(ci)],[0 yy(ci)],'r');
        pause(0.5);
end
legend('raw','smoothed')
hold off

[JooYoung Jeon]

Thank you so much!!

[Mathieu NOE]

My pleasure !

would you mind accepting my answer ?

tx