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To do such a test you need pink noise as a sound reference
Yes, but I call this "while noise". Freq sweep from 0 to 22050 could fit fine to.
It depends on the spectrum analyser. A true audio spectrum analyser (logarithmic power/bandwidth) would need a pink noise in order to return a flat response, a white noise would not be flat. But this is quite non-existent on PCs. I tried all Winamp plugins two or three years ago, plus SoundForge, CoolEdit, Wavelab, Samplitude, and an expensive dedicated spectrum analysis software, all were flat with white noise (constant power/bandwidth scaling).
The first spectrum analyser with the logarithmic power/bandwidth option that I saw was Magix Samplitude 6's one. Maybe SoundForge, CoolEdit etc have included this option in their latest versions too.
Without it, the spectrum is very far from what we hear. We see only bass.
White noise : noise whose spectrum has a constant level over frequency.
Pink noise : noise with the same power in each octave, that is the same power in each audio band. Each octave being twice as wide as the previous, its true spectrum is decreasing 3 db each octave.
Note that both scalings return a flat response with a sweep tone.