Re: How was it known that mics were good before the advent of hi-fi playback?

The definition of the calculated FFT coefficients is equivalent to a
bank of narrowband filters with the center frequencies translated to
DC. You can't do an FFT without calculating a bank of filters, what
you do with the coefficients is up to the user.

An utter misconception of what's going on.

I think you are simply ignorant of what is going on and the
applications and established practices. Filterbanks arejust another
useful valid interpretation of the DFT/FFT algorithm:

https://ccrma.stanford.edu/~jos/sasp/DFT_Filter_Bank_I.html

The algorithm works
the same whether the signal fed to it consists of stationary sinusoids
or noise. The coefficients are better for determining the parameters
of the sinusoids than for determining the parameters of a noise
process, but the analysis is still a Fourier analysis.

AAARRRGGGHHH!

Noise measurement is one of the classic applications of the DFT:

https://ccrma.stanford.edu/~jos/st/Power_Spectral_Density_Estimation.html

It is amazing how people can utterly pervert the meaning of facts, then
insist they're right.
...

It's sad that you find such useful applications of the facts so
painful and confusing.

I still say you don't understand what the Fourier transform is all about.
However, I can see how one might analyze a /time-limited/ noise signal.

.

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