Trying to combine two IR spectra where x is wavenumber (cm-1) and y is transmittance (0 to 1), having trouble.

I am trying to combine two IR spectra from a data base, they are being treated as two components. I want to add them together and plot it and make it into a single spectrum. The problem with this is the number of rows in one set is not the same as the other. The other problem is that the x (wavenumber) values for the two spectra are not the same (spacing is different). I can plot them superimposed, but I want to add them as a linear combination.

Answer 1

[Voss]

You'll can interpolate the two spectra onto a common set of wavenumbers. Then you can add the interpolated spectra together. Here's an example:

% some made-up data
x1 = linspace(650,700,6);
y1 = -0.25*sind(x1);
x2 = linspace(645,705,8);
y2 = 0.2*cosd(x2);

% plot the two curves
figure
plot(x1,y1,'.-b',x2,y2,'.-r')

% interpolate each y on a common set of x values,
% in this case the union of the two x vectors
x = union(x1,x2);
y1i = interp1(x1,y1,x);
y2i = interp1(x2,y2,x);

% add the interpolated values together
y = y1i+y2i;

% plot the interpolated values
hold on
plot(x,y1i,'bo',x,y2i,'ro')

% plot the sum
plot(x,y,'o-k')

% make a legend
legend({'y1','y2','y1i','y2i','y1i+y2i'},'Location','best','NumColumns',5)

% vertical lines showing how the x of each original curve
% maps to an x in the sum curve
xline(x,'--','Color',[0.7 0.7 0.7],'HandleVisibility','off');

Answer 2

[Star Strider]

It would help to have the data.

The best way is probably to interpolate the longer series to the length of the shorter series. They do not seem to have different names, so I would do something like this, using the resample function —

short_series(:,1) = linspace(651, 900, 397).';
short_series(:,2) = sin(2*pi*(short_series(:,1)-short_series(1,1))*0.01);
long_series = linspace(633, 910, 707).';
long_series(:,2) = sin(2*pi*(long_series(:,1)-long_series(1,1))*0.01);

figure
plot(short_series(:,1), short_series(:,2))
hold on
plot(long_series(:,1), long_series(:,2))
hold off
grid

res2 = resample(long_series(:,2), size(short_series,1), size(long_series,1)).';         % Use  'resample'

res2 = 1x397

0.0031 0.0432 0.0877 0.1311 0.1747 0.2176 0.2603 0.3024 0.3441 0.3849 0.4250 0.4644 0.5028 0.5403 0.5767 0.6120 0.6461 0.6790 0.7106 0.7408 0.7695 0.7968 0.8226 0.8467 0.8693 0.8901 0.9093 0.9267 0.9423 0.9561

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figure
plot(short_series(:,1), short_series(:,2))
hold on
plot(short_series(:,1), res2)
hold off
grid

Resampling the longer series to the length of the shorter series, instead of the other way round, avoids creating data in the shorter series where none previusly existed.

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