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Extracting a frequency band from a power spectrum

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ali8

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I have a time-domain signal, and then I applied some Power Spectral Density methods (e.g. Welch's) to find the PSD (i.e. the power spectrum). This power spectrum, in my case, ranges from ~ 0 to 8 Hz.

I want to extract certain bands from this spectrum, e.g. first band is 1-2 Hz, second is 2-4 Hz, then 4-8 Hz.

What I have is an array (in c++) containing that spectrum, and another array containing the corresponding freq. signal. Can I simply (and naively) extract those points in the spectrum corresponding to those points in the freq. signal from, say, 1-2 Hz, just like that? I mean, no need for any kind of filtering or such?
 

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