Find discontinuities and lift up or pull down the part after the discontinuity

13 Dec 2021
2 Answers
Answer Accepted
Updated 24 Dec 2021
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Hi everyone i have a singal with discontinuities.Does anyone know how can i find the discontinuities and at those points lift up or pull down the remaining signal?

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Jan
Jan on 13 Dec 2021
Please post some real data. The diagram is not clear enough. What is the width of the jumps? Is this one time step? What about using a low pass filter?
lena kappa
lena kappa on 13 Dec 2021
Sorry!
This is one of my datasets (my x axes is just 1:800)
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which gives me this
Jan
Jan on 14 Dec 2021
I do noit see the steps in your diagram.

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 Accepted Answer

Jan
Jan on 13 Dec 2021
Ran in:

1 vote

Ran in:
x = linspace(1, 10*pi, 200);
y = sin(x);
y(60:90) = y(60:90) + 1;
y(120:180) = y(120:180) - 1;
yOrig = y;
limit = 0.2;
dy = [0, diff(y)];
jump = strfind(abs(dy) > limit, [false, true, false]);
for ijump = 1:numel(jump)
k = jump(ijump);
y(k+1:end) = y(k+1:end) - dy(k+1);
end
figure
axes('NextPlot', 'add')
plot(x, yOrig, '-r', x, y, 'bo')
y2 = lowpass(y, 30, 200);
plot(x, y2, 'c+')

8 Comments
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lena kappa
lena kappa on 14 Dec 2021
Could you explain to me how this code works?
Jan
Jan on 14 Dec 2021
Edited: Jan on 14 Dec 2021
@lena kappa: The code searchs for steps greater than the limit. Then it deletes the height of the step from the rest of the vector.
lowpass is a low pass filter: A sharp step is a hight frequency signal. Lettting only low frequencies pass, removes jumps.
lena kappa
lena kappa on 20 Dec 2021
Edited: lena kappa on 23 Dec 2021
Hi @Jan i modified your code this way
x_0 = [1 800];
y_0 = [1 501.06];
y = improfile(img101,x_0,y_0)
yOrig = y;
limit = 0.2;
dy = [0, diff(y)];
jump = strfind(abs(dy) > limit, [false, true, false]);
for ijump = 1:numel(jump)
k = jump(ijump);
y(k+1:end) = y(k+1:end) - dy(k+1);
end
figure
axes('NextPlot', 'add')
plot(x, yOrig, '-r', x, y, 'bo')
y2 = lowpass(y, 30, 200);
plot(x, y2, 'c+')
and i get the next error:
Error using horzcat
Dimensions of arrays being concatenated are not consistent.
Error in lowpass_discontinuities_simple (line 34)
dy = [0, diff(y)];
do you know why?
lena kappa
lena kappa on 20 Dec 2021
Edited: lena kappa on 23 Dec 2021
all my code is :
img101 = imread('c1=100.800.1.0.1.png');
img_rot= imrotate(img101,32.06);
prof_img_rot(1:256,i)=img_rot(212+i,400:655)';
x_0 = [1 800];
y_0 = [1 501.06];
y = improfile(img101,x_0,y_0)
yOrig = y;
limit = 0.2;
dy = [0, diff(y)];
jump = strfind(abs(dy) > limit, [false, true, false]);
for ijump = 1:numel(jump)
k = jump(ijump);
y(k+1:end) = y(k+1:end) - dy(k+1);
end
figure
axes('NextPlot', 'add')
plot(x, yOrig, '-r', x, y, 'bo')
y2 = lowpass(y, 30, 200);
plot(x, y2, 'c+')
Jan
Jan on 23 Dec 2021
The command
dy = [0, diff(y)];
is working, if y is a row vector. For a column vector replace the comma by a semicolon for a horizontal concatenation:
dy = [0; diff(y)];
lena kappa
lena kappa on 23 Dec 2021
@Jan how did you choose the numbers 30 and 200 in
y2 = lowpass(y, 30, 200);
Jan
Jan on 24 Dec 2021
@lena kappa: See the documentation of lowpass:
y = lowpass(x,fpass,fs) specifies that x has been sampled at a rate of fs hertz. fpass is the passband frequency of the filter in hertz.
The result is stable over a wide range of parameters.

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More Answers (1)

Image Analyst
Image Analyst on 13 Dec 2021

0 votes

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lena kappa
lena kappa on 14 Dec 2021
Hello and thanks for your response hiw do you choose a and b in your code?
% Create uncorrupted data as a noisy sine wave.
x = linspace(pi/4,pi/2,60);
Y = sin(x) + randn(size(x))/80;
% plot(X, Y, 'b--s', 'LineWidth', 2);
% hold on
% Lower a chunk of it.
a=1.1; %unknown
b=-0.5; %unknown
I = 1 <= x & x <= 1.3; %KNOWN
Image Analyst
Image Analyst on 14 Dec 2021
@lena kappa That's not my code. You'd have to ask the author of the code.
lena kappa
lena kappa on 14 Dec 2021
But you uploaded this code in the link you sent above.
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 15;
% Create uncorrupted data as a noisy sine wave.
x = linspace(pi/4,pi/2,60);
Y = sin(x) + randn(size(x))/80;
% plot(X, Y, 'b--s', 'LineWidth', 2);
% hold on
% Lower a chunk of it.
a=1.1; %unknown
b=-0.5; %unknown
I = 1 <= x & x <= 1.3; %KNOWN
Yc = Y;
Yc(I) = a*Y(I)+b; %corrupted signal
% Plot original signal.
subplot(2, 1, 1);
plot(x, Yc, '--s', 'LineWidth', 2);
grid on;
xlabel('x', 'FontSize', fontSize);
ylabel('y', 'FontSize', fontSize);
title('Original Signal', 'FontSize', fontSize);
% Now we have data and we can begin.
%======================================================
% Get a smoothed signal
windowSize = 31;
ym = movmax(Yc, windowSize);
% Plot it.
hold on;
plot(x, ym, '-', 'LineWidth', 2);
% Find the difference between smoothed and actual
diffSignal = abs(ym - Yc);
plot(x, diffSignal, '-', 'LineWidth', 2);
% The lowered signal is where the difference is more than 3
% Get the good data.
threshold = 0.3;
yline(threshold, 'Color', 'g', 'LineWidth', 3);
goodIndexes = diffSignal < threshold;
badIndexes = diffSignal >= threshold;
xGood = x(goodIndexes);
yGood = Yc(goodIndexes);
% Interpolate over the bad section.
ym = interp1(xGood, yGood, x);
% Plot the interpolated section
plot(x, ym, 'm-');
% Update the difference signal.
diffSignal = abs(ym - Yc);
% Get average difference over ths bad section
amountToLift = mean(diffSignal(badIndexes))
% List bad data.
yRepaired = Yc; % Initialize
yRepaired(badIndexes) = Yc(badIndexes) + amountToLift;
% Plot repaired signal.
subplot(2, 1, 2);
plot(x, yRepaired, 'g.-', 'LineWidth', 2, 'MarkerSize', 20);
grid on;
xlabel('x', 'FontSize', fontSize);
ylabel('y', 'FontSize', fontSize);
title('Repaired Signal', 'FontSize', fontSize);
g = gcf;
g.WindowState = 'maximized';
lena kappa
lena kappa on 14 Dec 2021
i think i understood it! sorry to bother you again
Image Analyst
Image Analyst on 15 Dec 2021
I guess those were just some parameters to cause a chunk of the waveform to shift by a reasonable amount.

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Asked:

lena kappa
lena kappa
on 13 Dec 2021

Commented:

Jan
Jan
on 24 Dec 2021

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