Question

The bit rate for a signal, which has a sampling rate of $8\,kHz$ and where 16 quantisation levels have been used is:
A. $32000\,bits/\sec$
B. $16000\,bits/\sec$
C. $64000\,bits/\sec$
D. $72000\,bits/\sec$

Answer 1

In order to answer this question, to find the bit rate, we have to find the number of bits per sample first and then we will convert the sample rate of $8kHz$ in the unit of $Hz$ . And then at last we will apply the formula to find the bit rate in terms of sample rate.

Complete step by step answer:
If $n$ is the number of bits per sample, then number of quantisation level is 2,
Since, the number of quantisation level is 16:-
${2^n} = 16 \\\ \Rightarrow n = 4$
Sample rate $= 8kHz = 8000Hz$
$\text{Bit rate} = \text{Sampling rate} \times \text{Number of bits per sample} \\\ \Rightarrow \text{Bit rate}= 8000 \times 4 \therefore \text{Bit rate}= 32000\,bits/\sec \\\$
Hence, the correct option is A.

Additional Information: The rate at which data is processed or conveyed is referred to as bit rate. It is commonly measured in seconds, with smaller numbers ranging from bps to kbps and mbps. Bit rate is often referred to as data rate or bitrate. The sample rate refers to the number of times an audio sample is taken in a second: the number of times per second that recording equipment converts sound into data. The sampling rate for most digital audio is $44.1\,kHz$ , which is also the sampling rate for audio CDs. This indicates that during recording, the audio is sampled $44,100{\text{ }}times{\text{ }}per{\text{ }}second$ .

Note: There is another way to calculate the bit rate. The formula for calculating the bit rate is: ${\text{Frequency}} \times \text{bit depth} \times \text{channel} = \text{bit rate}$ . The sample rate of a typical uncompressed high-quality audio file is 44,100 samples per second, with a bit depth of 16 bits per sample and two stereo channels.