MATLAB: How do you transfer this signal into linear form

data importimportlinearnonlinearstudentundergraduate

my starting code is below. I must now convert this signal and make it linear. Any ideas on how to achieve this?

A = dlmread('signal_2.txt'); %Reads signal data file

x= A(:,1); %Time Variables

y= A(:,2); %Amplitude variables

Many Thanks

Many Thanks!

Best Answer

I see this is a follow up to your previous question which was answered in https://www.mathworks.com/matlabcentral/answers/506414-how-do-you-separate-imported-data-into-time-and-amplitude

The approach in the earlier post to to remove the linear trend the data was:

% make regression matrix, A where

% y = A*c + error

A = [x(:) ones(size(x(:)))]
% Find least squares solution (regression) for constants c that provide best fit for

% y = c(1)*x + c(2) using Matlab \ operator
c = A\y
% remove the linear growth (detrend) the data
yDetrended = y - (c(1)*x + c(2))
% plot the result

plot(x,yDetrended)

Looking at your new dataset signal_2.txt, it looks like the data now has a parabolic (quadratic) trend to remove.

You could modify the previous approach to instead fit a quadratic curve to the data and then subtract it off.

% make regression matrix, A where
% y = A*c + error
A = [x(:).^2 x(:) ones(size(x(:)))]
% Find least squares solution (regression) for constants c that provide best fit for
% y = c(1)*x^2 + c(2)*x + c(3) using Matlab \ operator
c = A\y
% remove the quadratic trend from the data
yDetrended = y - A*c % note A*c = (c(1)*x.^2 + c(2)*x + c(3)) 
figure
% plot the result
plot(x,yDetrended)

p.s. If you have a signal_3.txt that has a cubic trend, I think you can figure out what to do from here :)

Related Solutions

MATLAB: How do you separate imported data into time and amplitude

If by detrend you mean that you want to remove the part of the signal that is growing linearly with time then the expression you have will not work. It will just shift your whole plot horizontally, so that it is centered on the mean value for the whole series.

Instead you can do a little linear regression to find the best straight line (y = mx + b) through the data, and then subtract that off.

To do this in MATLAB you could use:

% make regression matrix, A where
% y = A*c + error
A = [x(:) ones(size(x(:)))]
% Find least squares solution (regression) for constants c that provide best fit for
% y = c(1)*x + c(2) using Matlab \ operator
c = A\y
% remove the linear growth (detrend) the data
yDetrended = y - (c(1)*x + c(2))
% plot the result
plot(x,yDetrended)

Here is a good link to learn more about the linear regression, https://www.mathworks.com/help/matlab/data_analysis/linear-regression.html

MATLAB: Shifting Baselines of Raman Spectra

This is an interesting problem!

It took me a while to figure out the correct approach, however it is deceptively simple, and uses only core MATLAB functions (although it requires R2017b or later for the ischange function). The essence of it is to use the 'linear' option of ischange to get the slopes of the various line segments, then use hiscounts to find the most numerous slopes, corresponding to the linear baseline of your Raman signal data. After that, it¹s just a polyfit call to calculate the slope of the line to be detrended. It requires a bit of interaction at the outset to do the initial thresholding, with the rest taking care of itself.

The Code —

D = csvread('raman-1 week.csv');
x = D(:,1);
y = D(:,2);
x = x(y >= 1E+4);                                           % Threshold Data

y = y(y >= 1E+4);                                           % Threshold Data
[Cp,Sl,Ic] = ischange(y,'linear');                          % Detect Changes, Calculates Slopes (& Intercepts)
[Cts,Edg,Bin] = histcounts(Sl, 50);                         % Histogram Of Slopes
[Max,Binmax] = max(Cts);                                    % Find Largest Bin
LinearRegion = (Bin==Binmax);                               % Logical Vector Of Values Corresponding To Largest Number Of Slopes
B = polyfit(x(LinearRegion), y(LinearRegion), 1)            % Linear Fit
L = polyval(B, x);                                          % Evaluate
yc = y - L;                                                 % Detrend
figure
plot(x, yc)
grid

The Plot —

That’s likely as close as it’s possible to get. I encourage you to experiment with it to fine-tune it to your requirements.

For comparison, the original signal is:

Best Answer

Related Solutions

MATLAB: How do you separate imported data into time and amplitude

MATLAB: Shifting Baselines of Raman Spectra

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