Evaluate the value of signal-to-quantization noise ratio

Question

Assignment:

1. Given the signal

a(t) = 20 cos (100πt) + 17cos(500πt).

How many bits are necessary to achieve a signal-to-quantization noise ratio greater than 45 dB using a uniform quantizer? Using a standard µ-law technique, how many bits are necessary to achieve a signal-to-quantization noise ratio greater than 50 dB?

2. The signal a(t) is obtained by filtering the periodic square wave b(t) with period Tp = 10^-3 s and zero mean

b(t) = Σ^+∞ _{k= -∞} [rect (t - kT_p / T_p/2) - rect (t - kT_p - T_p/2 / T_p/2)]

through an ideal lowpass filter with bandwidth 5.1 kHz. The signal a(t) is applied to a quantizer with 6 bits. Evaluate the value of the signal-to-quantization noise ratio when the quantizer has

a) Uniform characteristic.

b) Nonuniform characteristic with standard µ-law companding.