Consider a uniform quantizer characterized by the input—output relation illustrated Figure a. Assume that a Gaussian-distributed random variable with zero mean and unit variance is applied to this quantizer input.

(a) What is the probability that the amplitude of the input lies outside the range -4 to +4?

(b) Using the result of part (a), show that the output signal-to-noise ratio of the quantizer is given by (SNR) O = 6R — 7.2 dB, where R is the number of bits per sample. Specifically, you may assume that the quantizer input extends from —4 to +4, Compare the result of part (b) with that obtained in Example 3.1.