Human ear - freq log scale I am not sure if it's DSP question or physic.

But I wonder is there any math equation (method) that describe that graph? (It could be anything approximately like that).

I am working on audio freq analyser. And for typical pop song I get graph that Low End is very big but Middle and High End are very low. That's the mathematical reality, but I want to transform it to human ear reality. Could anyone help me?

(Of course I know how to make freq log scale on horizontal axis and dB scale on vertical axis, just have problem to modify it to human ear characteristic)
So Robert Wannamaker did a real bang-up job parameterizing the 0 dB curve and came up with, what he called F-weighting.  It's in this AES paper from the 90s:



you can see that this can be turned into an $H(s)$, and with the bilinear transform, into an $H(z)$.

here is the curve on a dB vs. log/linear freq scale.  the log frequency plot is the upside-down version of your 0 dB curve above but is more updated from Fletcher-Munson to the ISO standard which cam from i dunno where.



here's a table of poles and zeros: