Let $X(t)=A \cos \left(2 \pi f_{0} t+\theta\right)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distributed in the intervals $[-2,2]$ and $[0,2 \pi]$, respectively. $X(t)$ is fed to an 8-bit uniform mid-rise type quantizer. Given that the autocorrelation of $X(t)$ is $R_{X}(\tau)=\frac{2}{3} \cos \left(2 \pi f_{0} \tau\right)$, the signal to quantization noise ratio (in $\mathrm{dB}$, rounded off to two decimal places) at the output of the quantizer is $\_\_\_\_\_\_$.
