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A speech signal occupying the bandwidth of 300 Hz to 3 kHz is converted into PCM format for use in digital communication. If the sampling frequency is8 kHz and each sample is quantized into 256 levels, then the output bit the rate will be
- a)3 kb/s
- b)8 kb/s
- c)64 kb/s
- d)256 kb/s
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A speech signal occupying the bandwidth of 300 Hz to 3 kHz is converte...
fs = 8 kHz, 2n = 256 or n = 8. Bit Rate = 8 x 8k = 64 kb/s.
Most Upvoted Answer
A speech signal occupying the bandwidth of 300 Hz to 3 kHz is converte...
Signal Bandwidth:
The speech signal occupies a bandwidth of 300 Hz to 3 kHz. This means that the frequency range of the speech signal lies between 300 Hz and 3 kHz.
Sampling Frequency:
The sampling frequency is given as 8 kHz. This means that the speech signal is sampled at a rate of 8,000 samples per second.
Quantization Levels:
Each sample of the speech signal is quantized into 256 levels. This means that each sample value can be represented using 8 bits (2^8 = 256).
Calculation:
To calculate the output bit rate, we need to consider the sampling frequency and the number of bits per sample.
Number of Bits per Sample:
Since each sample is quantized into 256 levels, it can be represented using 8 bits. Therefore, the number of bits per sample is 8.
Number of Samples per Second:
The sampling frequency is given as 8 kHz, which means that 8,000 samples are taken per second.
Output Bit Rate:
To calculate the output bit rate, we multiply the number of samples per second by the number of bits per sample.
Output Bit Rate = Number of Samples per Second x Number of Bits per Sample
= 8,000 samples/second x 8 bits/sample
= 64,000 bits/second
= 64 kb/s
Therefore, the output bit rate for the given speech signal in PCM format is 64 kb/s.
The speech signal occupies a bandwidth of 300 Hz to 3 kHz. This means that the frequency range of the speech signal lies between 300 Hz and 3 kHz.
Sampling Frequency:
The sampling frequency is given as 8 kHz. This means that the speech signal is sampled at a rate of 8,000 samples per second.
Quantization Levels:
Each sample of the speech signal is quantized into 256 levels. This means that each sample value can be represented using 8 bits (2^8 = 256).
Calculation:
To calculate the output bit rate, we need to consider the sampling frequency and the number of bits per sample.
Number of Bits per Sample:
Since each sample is quantized into 256 levels, it can be represented using 8 bits. Therefore, the number of bits per sample is 8.
Number of Samples per Second:
The sampling frequency is given as 8 kHz, which means that 8,000 samples are taken per second.
Output Bit Rate:
To calculate the output bit rate, we multiply the number of samples per second by the number of bits per sample.
Output Bit Rate = Number of Samples per Second x Number of Bits per Sample
= 8,000 samples/second x 8 bits/sample
= 64,000 bits/second
= 64 kb/s
Therefore, the output bit rate for the given speech signal in PCM format is 64 kb/s.
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