Question

5.2-3 In a satellite radio system, 500 stations of stereo quality are to be multiplexed in one data stream. For each station, two (left and right) signal channels each of bandwidth 15, 000 Hz are sampled, quantized, and binary-coded into PCM signals. (a) If the maximum acceptable quantization error in sample amplitudes is 1% of the peak signal voltage, find the minimum number of bits needed for a uniform quantizer.

Answer 1

the minimum number of bits needed for quantization is 7

Explanation:

Given the data in the question;

if quantization is Δv, then the maximum quantization Error is Δv/2

now if we split up the whole range from -
`m_(p)` to
`m_(p)` evenly into L levels, so

Δv =
`2m_(p)` / L

Δv / 2 =
`m_(p)` / L

given that the error must be at most 1% of
`m_(p)`,

1%
`m_(p)` =
`m_(p)` / L

1/100 ×
`m_(p)` =
`m_(p)` / L

100 = L

now L must be a factor of 2 to be binary encoded,

so lets consider;

L = 128

2ⁿ = 128¹

2ⁿ = 2⁷

n = 7

Therefore, the minimum number of bits needed for quantization is 7