Evaluate the statistical power of the saturation noise

Question

Assignment:

1. Evaluate the statistical power of the saturation noise, ^Me_sat using a three-bit uniform quantizer with Gaussian input a(t) with zero mean and variance σ²a Assume v_sat = 3σ_a.

2. Find the number of bits necessary to achieve the signal-to-quantization noise ratio of 60 dB, using a uniform quantizer with a Gaussian input and imposing a saturation probability of 10-3.

3. Consider a four-bit uniform quantizer with dynamic range (0, 1) V. Assuming the input signal a(t) = 20 cos(2Πƒ₀t):

a) Determine the pre-processing needed to adapt the signal to the quantizer.

b) Find the codewords corresponding to the input values -1.58 V and 5.22 V.

c) Find the signal-to-quantization noise ratio A_q.