Computation of the bandwidth of a spectrum in wavelength domain

I have a spectrum that is plotted in the wavelength domain, and I need to find the bandwidth of the spectrum. I can't share the full code else, it will be overwhelming, so I saved the vectors. The bandwidth that the obw() function gives is innacurate. Please how can I find the correct bandwidth?

clear
filename1 =  'Ab.txt';
filename2 =  'lambda_axis.txt';
Ab = importdata(filename1);
lambda = importdata(filename2);
lambda_range = (lambda>1100e-12 & lambda<2000e-12);
plot(lambda(lambda_range),Ab(lambda_range));
xlim ([1.2e-9 1.9e-9]);
bw = obw(Ab,lambda);

[David Goodmanson]

Hello Ikechi,

the lambda file has some issues. The lower half of the file has decreasimg negative values for lambda, the upper half has decreasing positive values. In the middle there is a discontinuity where lambda changes sign. Something needs to be changed.

[Ikechi Ndamati]

I doubt if that is the issue because even when i use this, it still gives inaccurate results

bw = obw(Ab(lambda_range),lambda(lambda_range));

[David Goodmanson]

ok the lambda_range data has no problem but the obw result is negative, and (assuming you are staying in the wavelength domain) it appears to be on the large side by about a factor of 2. Is that the inaccuracy you have in mind?

[Ikechi Ndamati]

@David Goodmanson I do not expect a 100% accuracy. However, the current bandwidt values are not even remotely close to a reasonable value. I need to know why my implementation gives unreasonable values so that I can try to solve the issue.

Answer 1

[David Goodmanson]

Hi Ikechi,

the problem is basically that there are not enouch points to work with.

lambda = lambdaaxis;
lambda_range = (lambda>1100e-12 & lambda<2000e-12);
lam1 = lambda(lambda_range);
A1 = Ab(lambda_range);
bw = obw(A1,lam1)
       % bw = -8.8591e-10
% add a lot of interpolated points
a = min(lam1);
b = max(lam1);
lamnew = linspace(a,b,10000);
Anew = interp1(lam1,A1,lamnew);
figure(1); grid on
plot(lamnew,Anew)
bw1 = obw(Anew,lamnew)
      % bw1 = 4.2769e-10

[Ikechi Ndamati]

@David Goodmanson Thank you very much. This gives a realistic answer.

On a different note, I want to ask how you knew that this would be the solution. Is it based on your experience or is there any MATLAB documentation out there that I failed to read? Maybe is there any place that explains the intricacies of most functions? Because it seems that for you to know how to scale through some of these issues, one must know the internal workings of the MATLAB functions. If there is any such available material, please point it to me.

Thanks again

[David Goodmanson]

Hi Ikechi,

I didn't really know that it would work, I just tried it. One of the great things about Matlab is since it's an interpreted language, it's easy to try stuff. There was some reason to believe that the number of points might be involved, though. Lambda_range has 245 points. obw says it uses periodogram, and periodogram says it uses a minimum of 256 points, so increasing the number of points seemed like a worthwhile exercise.

[Ikechi Ndamati]

Hello David, that's smart.

Thanks for the insight. I will apply this tactics in future problems.