Calculating the bandwidth of multi variable function

Dear all, I have the following gain spectrum

 y=(1./((f.^2)+1))-(p./((f+w).^2+1))-(p./((f-w).^2+1));

I evaluated the function over the variables f, w and p. Now I want find the 3db-bandwidth of resulting spectrum over certain values of f, lets say(f1= -0.5,f2=0.5) * only* and not over the entire period. Afterwards, I want to plot the bandwidth against p and w , and find the SNR Thank you

   N = 200 ;

    f = linspace(-4,4,N) ;

    p = linspace(0,1,N) ;

    w = linspace(0,2,N) ;

    [f,p,w] = meshgrid(f,p,w) ;

    y=(1./((f.^2)+1))-(p./((f+w).^2+1))-(p./((f-w).^2+1));

[KALYAN ACHARJYA]

What is x? f1=-4 and f2=200 then bandwidth 204, your comment?

[Alin Brad]

I revised the question

[KALYAN ACHARJYA]

Your question is not clear to me.

[Alin Brad]

since this function may has many peaks over the entire period (-4,4), I want to find the 3db bandwidth of certain portion this function over the period (-0.5,0.5)

[Walter Roberson]

Are you talking about FWHM (Full Width at Half Maximum) ?

[Alin Brad]

Yes exactly. However, the required bandwidth FWHM only over certain range of f (-0.5,0.5)

[Walter Roberson]

FWHM code could perhaps be adapted from https://www.mathworks.com/matlabcentral/answers/407722-how-do-i-calculate-fwhm-from-gaussian-fitted-curve#answer_326569

You could feed in only the data corresponding to that range -- unless, that is, doing so would affect the calculation of where the baseline was.