Question

A telephone line must have a Quantization SNR above 27 dB, what is the minimum number of bits per sample?

A) 3 bits
B) 4 bits
C) 4.5 bits
D) 5 bits
E) 5.5 bits

Answer 1

To achieve a minimum quantization SNR above 27 dB for a telephone line, one must use at least 5 bits per sample to encode the signal as it provides an SNR that meets the minimum requirement.

Step-by-step explanation:

The SNR (Signal-to-Noise Ratio) quantization can be calculated using the formula SNR = 6.02n + 1.76 dB, where n represents the number of bits per sample. To achieve an SNR above 27 dB, we have to solve for n. By rearranging the formula, we get n = (SNR - 1.76) / 6.02. Plugging in the required SNR of 27 dB gives us:

n = (27 - 1.76) / 6.02

n = 4.19 bits

Since the number of bits per sample must be a whole number, we must round up to the nearest whole bit. Therefore, the minimum number of bits per sample is 5 bits (Option D).