GATE 2024 EC – Question 57

Let $X(t)=A\cos(2\pi f_0t+\theta)$ 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 $R_X(\tau)=\dfrac23\cos(2\pi f_0\tau)$, the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is ________.