GATE 2018 IN Q.53: solution and answer

GATE 2018 · INQ.53 · 2 marks · NAT

The sampling rate for Compact Discs (CDs) is 44,000 samples/s. If the samples are quantized to 256 levels and binary coded, the corresponding bit rate (in bits per second) is _____.

See the question in the paper

Tap to open full size

Answer and solution

ANSWER

The bit rate is $352, 000 bits/s$ .

Official answer: 352000Source: Official answer key, GATE 2018 IN (IIT Guwahati)

Each sample is quantized to $256$ levels. With binary coding, the number of bits per sample is $n = lo g_{2} 256 = 8$ .
The bit rate is the sampling rate times the bits per sample: $R_{b} = f_{s} \cdot n$ .
$R_{b} = 44, 000 \times 8 = 352, 000 bits/s$ .

KEY IDEA

Bit rate of a PCM stream equals the sampling rate times the number of bits per sample, where the bits per sample is $lo g_{2}$ of the number of quantization levels.

WATCH OUT FOR

Using the number of levels (256) in place of the number of bits (8), or multiplying $f_{s}$ by $lo g_{2} 256$ and forgetting the 44,000 figure is the sampling rate itself, not a bandwidth that needs doubling.

From the GATE 2018 IN paper. Every question of this paper · Download the full paper · All 15 Digital communication questions, with notes

GATE 2018 IN Q.53: solution and answer

Answer and solution

More Digital communication questions