MATLAB: Zeroeing baseline & measuring noise in noisy signal

signal processing

I am analysing voltage signal acquired at 40KHz sampling frequency, my aim is to detect an event at an exact time, I attach example. I have 2 questions regarding signal processing.

1. What is the most appropriate way to zero the signal?

I tried subtracting the mean measured in a window of variable lengths – anything from 40 to 4000 points. But as you can see the signal is quite noisy with lots of spontaneous events, so at times if the window happens to include lots of events the mean will be affected and the zeroing will not work as well.

2. How to best measure the standard deviation of baseline noise?

To establish if anything occurred at my timepoint of interest, I would like to measure baseline noise standard deviation, and set a criterion that if the peak of the event of interest is larger than 4*standard deviation of the noise then the event has occurred. However, again, because the signal is so noisy, I am not sure how to approach measuring baseline noise.

I am new to signal processing, and I want to make sure I am not making any silly mistakes, any input will be much appreciated!

Best Answer

There is noise everywhere - on the low valleys and even on the high peaks. If you want you can just set a threshold and zero out the signal if it falls below some threshold:

signal(signal < someValue) = 0;

or you can try to smooth the whole thing with sgolayfilt(). See attached demo.

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MATLAB: How to straighten a sinusoidal signal

It looks like the signal is going along just fine until suddenly there is a big jump, and then it's fine again. So rather than filter the whole signal, I'd just identify the jump locations, determine the new offset, and subtract that from the signal. Here is the code. It's s fast and simple for loop.

% Initialization steps.
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 = 20;
xy = xlsread('capture 2.xls');
x = xy(:, 1);
y = xy(:, 2);
subplot(3, 1, 1);
plot(x, y, 'b-');
grid on;
title('Original Signal', 'FontSize', fontSize);
subplot(3, 1, 2);
differences = [0; diff(y)];
plot(x, differences, 'b-');
grid on;
title('Difference Signal', 'FontSize', fontSize);
offset = 0;
for k = 1 : length(y)
  if abs(differences(k)) > 0.001
    offset = differences(k);
  end
  correctedSignal(k) = y(k) - offset;
end
subplot(3, 1, 3);
plot(x, correctedSignal, 'b-');
title('Corrected Signal', 'FontSize', fontSize);
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);

I think it does a pretty good job, don't you?

MATLAB: How to close the gaps

Stelios, since you didn't provide me with the original image I had to take a screenshot and try to fix it up in Photoshop. Then I thresholded, blurred, rethresholded, scanned for the top row, and overlaid it on the original image. Code is below. Let me know if you like it.

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 = 20;
%===============================================================================
% Read in gray scale demo image.
folder = pwd; % Determine where demo folder is (works with all versions).
baseFileName = 'sofar.jpg';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
  % The file doesn't exist -- didn't find it there in that folder.
  % Check the entire search path (other folders) for the file by stripping off the folder.
  fullFileNameOnSearchPath = baseFileName; % No path this time.
  if ~exist(fullFileNameOnSearchPath, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
rgbImage = imread(fullFileName);
% Get the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(rgbImage)
if numberOfColorChannels > 1
  % It's not really gray scale like we expected - it's color.
  % Use weighted sum of ALL channels to create a gray scale image.
  %   grayImage = rgb2gray(rgbImage);
  % ALTERNATE METHOD: Convert it to gray scale by taking only the green channel,
  % which in a typical snapshot will be the least noisy channel.
  grayImage = rgbImage(:, :, 1); % Take red channel.
else
  grayImage = rgbImage; % It's already gray scale.
end
% Now it's gray scale with range of 0 to 255.
% Display the image.



subplot(4, 1, 1);
imshow(grayImage, []);
title('Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hp = impixelinfo();
%------------------------------------------------------------------------------
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')
drawnow;
% Binarize the image
binaryImage = grayImage >= 3;
% Extract the largest blob only
binaryImage = bwareafilt(binaryImage, 1);
% Fill holes
binaryImage = imfill(binaryImage, 'holes');
% Display the image.
subplot(4, 1, 2);
imshow(binaryImage, []);
title('Binary Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hp = impixelinfo();
drawnow;
% Blur the image
windowWidth = 25;
blurredImage = conv2(double(binaryImage), ones(windowWidth)/windowWidth^2, 'same');
% Threshold again.
binaryImage = blurredImage > 0.5;
% Display the image.
subplot(4, 1, 3);
imshow(binaryImage, []);
title('Smoothed Binary Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hp = impixelinfo();
drawnow;
% Scan the image looking for the top most pixel.
topRows = rows * ones(1, columns); % Preallocate.
for col = 1 : columns
  thisTopRow = find(binaryImage(:, col), 1, 'first');
  if ~isempty(thisTopRow)
    topRows(col) = thisTopRow;
  end
end
% Display the image.
subplot(4, 1, 4);
imshow(grayImage, []);
title('Original Image with top rows overlaid', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hp = impixelinfo();
% Show top line over it.
hold on;
plot(topRows, 'r-', 'LineWidth', 2);

Best Answer

Related Solutions

MATLAB: How to straighten a sinusoidal signal

MATLAB: How to close the gaps

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