diff --git a/README.md b/README.md index d0ef1c5..c0edcc8 100644 --- a/README.md +++ b/README.md @@ -39,13 +39,21 @@ def compexp_gain( ``` $$ -x_{\rm rms}[n] = \alpha_{\rm rms} x^2[n] + (1 - \alpha_{\rm rms}) x_{\rm rms}[n-1] \\ -x_{\rm log}[n] = 20 \log_{10} x_{\rm rms}[n] \\ -g_{\rm log}[n] = \min\left(0, \left(1 - \frac{1}{CR}\right)\left(CT - x_{\rm log}[n]\right), \left(1 - \frac{1}{ER}\right)\left(ET - x_{\rm log}[n]\right)\right) \\ -g[n] = 10^{g_{\rm log}[n] / 20} \\ +x_{\rm rms}[n] = \alpha_{\rm rms} x^2[n] + (1 - \alpha_{\rm rms}) x_{\rm rms}[n-1] +$$ +$$ +x_{\rm log}[n] = 20 \log_{10} x_{\rm rms}[n] +$$ +$$ +g_{\rm log}[n] = \min\left(0, \left(1 - \frac{1}{CR}\right)\left(CT - x_{\rm log}[n]\right), \left(1 - \frac{1}{ER}\right)\left(ET - x_{\rm log}[n]\right)\right) +$$ +$$ +g[n] = 10^{g_{\rm log}[n] / 20} \hat{g}[n] = \begin{rcases} \begin{dcases} - \alpha_{\rm at} g[n] + (1 - \alpha_{\rm at}) \hat{g}[n-1] & \text{if } g[n] < g[n-1] \\ + \alpha_{\rm at} g[n] + (1 - \alpha_{\rm at}) \hat{g}[n-1] & \text{if } g[n] < g[n-1] \alpha_{\rm rt} g[n] + (1 - \alpha_{\rm rt}) \hat{g}[n-1] & \text{otherwise} -\end{dcases}\end{rcases} \\ +\end{dcases}\end{rcases} +$$ +$$ y[n] = \hat{g}[n] x[n] $$