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```math

\tau_r = \frac{C_{det} \cdot C_{out}}{g_m \cdot C_f}

```

The impulse response function of this transfer function is convoluted with the charge pulse. In the time domain, the impulse response function can be written

The impulse response function of this transfer function is convoluted with the charge pulse. In the time domain, the impulse response function can be written as

```math

\mathcal{L}^{-1}(H) = R_f \left( \frac{e^{-t/\tau_f}}{\tau_f - \tau_r} - \frac{e^{-t/\tau_r}}{\tau_f - \tau_r} \right).

```