# SNR of μ-law companding

I know the snr after μ-law compression is

$$\text{SNR}\approx\frac{3L^2}{[\ln(1+ \mu)]^2}$$ when $$\mu \gg \frac{\max_t m(t)}{\text{rms}(m(t))}$$,

where $$m(t)$$ is the message signal, and
$$L$$ the number of levels.

Can anyone give the idea how it came or the proof?

• I don't understand. Your "mp" or $a$ is both time-variant, so it needs to be $a(t)$, and it actually is the message signal $m(t)$, isn't it? – Marcus Müller Sep 10 '20 at 9:50
• mp is the maximum value of the message signal m(t) – Zemi Alvez Sep 10 '20 at 9:59