# Why is this version of Fourier deconvolution justiifed?

As I understand it, one typically performs Fourier deconvolution for the data produced by some instrument of a linear system by:

1. Taking the observation of some unit impulse signal $$m$$, with the property that every other input can be represented as the sum of scaled versions of $$m$$ - let's call the data of this observation $$s$$.

2. Taking the observation of the phenomenon we care about, let's call this $$o$$.

Then, we say that to go from $$m$$ to $$s$$ the instrument has convolved with some other function and then say, via certain remarkable properties of Fourier transforms and convolutions, that $$O = IS$$, where $$i$$ is the ideal data we wish to obtain from $$o$$ via deconvolution and capital letters denote the Fourier transform of a function.

The other day, a friend suggested the following in a situation related to measuring the spectra of certain light sources:

Because we couldn't measure a unit impulse signal, we should instead measure a known blackbody radiation curve, $$bbr$$, as the data $$s$$. Then, he said that "via a parallel" we see that for a general input $$i$$ to our system and a general output $$o$$ associated with that input, we have $$O = SI$$ and then you solve for $$I$$ using inverse fourier transforms.

I pointed out that it was definitely not known that $$bbr$$ could represent every other signal in the form of the superposition of scaled versions of itself and so that there was no reason I knew of for this to work. Given that they said "it was a form of genuine physical insight" and the fact that they are generally correct, I believe them - but why is what they said true?