An input to a $6$-level quantizer has the probability density function $f(x)$ as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that $3$ consecutive decision boundaries are $\text{‘-1’, ‘0’}$ and $\text{‘1’.}$
Assuming that the reconstruction levels of the quantizer are the mid-points of the decision boundaries, the ratio of signal power to quantization noise power is
- $\frac{152}{9}$
- $\frac{64}{3}$
- $\frac{76}{3}$
- $28$
