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An analog signal is sampled, quantized and encoded into a binary PCM system. The specifications of the PCM system include the following: Sampling role = 8 KHz Number of representation levels = 64
Determine the minimum bandwidth required if PCM wave is transmitted over a baseband channel.
Determine the minimum bandwidth required if PCM wave is transmitted over a baseband channel.
- a)64 KHz
- b)32 KHz
- c)24 KHz
- d)48 KHz
Correct answer is option 'C'. Can you explain this answer?
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PCM System and Bandwidth Calculation
PCM (Pulse Code Modulation) is a digital technique used to represent analog signals. The analog signal is first sampled, quantized, and then encoded into a binary PCM system. The specifications of the PCM system are as follows:
- Sampling rate = 8 KHz
- Number of representation levels = 64
The minimum bandwidth required for transmitting the PCM wave over a baseband channel is to be determined. Let's see how to calculate it.
Sampling Rate
The sampling rate determines how often the analog signal is sampled and converted into a digital signal. In this case, the sampling rate is given as 8 KHz, which means that the analog signal is sampled 8000 times per second.
Number of Representation Levels
The number of representation levels determines how many different values the quantized signal can take. In this case, the number of representation levels is given as 64, which means that the quantized signal can take 64 different values.
Bit Rate
The bit rate of a PCM system is calculated as follows:
Bit rate = Sampling rate x Number of bits per sample
In this case, the number of bits per sample can be calculated as follows:
Number of bits per sample = log2(Number of representation levels) = log2(64) = 6 bits
Therefore, the bit rate can be calculated as follows:
Bit rate = Sampling rate x Number of bits per sample = 8 KHz x 6 bits = 48 Kbps
Bandwidth Calculation
The bandwidth required for transmitting the PCM wave over a baseband channel can be calculated using the Nyquist formula, which states that the bandwidth required is equal to twice the highest frequency component present in the signal.
In this case, the highest frequency component present in the signal can be calculated as follows:
Highest frequency component = Sampling rate / 2 = 8 KHz / 2 = 4 KHz
Therefore, the bandwidth required can be calculated as follows:
Bandwidth = 2 x Highest frequency component = 2 x 4 KHz = 8 KHz
Since the PCM wave is transmitted over a baseband channel, the bandwidth required is equal to the bit rate. Therefore, the minimum bandwidth required is 48 Kbps or 24 KHz.
Conclusion
The minimum bandwidth required for transmitting the PCM wave over a baseband channel is 24 KHz, which is calculated based on the sampling rate, number of representation levels, and Nyquist formula.
PCM (Pulse Code Modulation) is a digital technique used to represent analog signals. The analog signal is first sampled, quantized, and then encoded into a binary PCM system. The specifications of the PCM system are as follows:
- Sampling rate = 8 KHz
- Number of representation levels = 64
The minimum bandwidth required for transmitting the PCM wave over a baseband channel is to be determined. Let's see how to calculate it.
Sampling Rate
The sampling rate determines how often the analog signal is sampled and converted into a digital signal. In this case, the sampling rate is given as 8 KHz, which means that the analog signal is sampled 8000 times per second.
Number of Representation Levels
The number of representation levels determines how many different values the quantized signal can take. In this case, the number of representation levels is given as 64, which means that the quantized signal can take 64 different values.
Bit Rate
The bit rate of a PCM system is calculated as follows:
Bit rate = Sampling rate x Number of bits per sample
In this case, the number of bits per sample can be calculated as follows:
Number of bits per sample = log2(Number of representation levels) = log2(64) = 6 bits
Therefore, the bit rate can be calculated as follows:
Bit rate = Sampling rate x Number of bits per sample = 8 KHz x 6 bits = 48 Kbps
Bandwidth Calculation
The bandwidth required for transmitting the PCM wave over a baseband channel can be calculated using the Nyquist formula, which states that the bandwidth required is equal to twice the highest frequency component present in the signal.
In this case, the highest frequency component present in the signal can be calculated as follows:
Highest frequency component = Sampling rate / 2 = 8 KHz / 2 = 4 KHz
Therefore, the bandwidth required can be calculated as follows:
Bandwidth = 2 x Highest frequency component = 2 x 4 KHz = 8 KHz
Since the PCM wave is transmitted over a baseband channel, the bandwidth required is equal to the bit rate. Therefore, the minimum bandwidth required is 48 Kbps or 24 KHz.
Conclusion
The minimum bandwidth required for transmitting the PCM wave over a baseband channel is 24 KHz, which is calculated based on the sampling rate, number of representation levels, and Nyquist formula.
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An analog signal is sampled, quantized and encoded into a binary PCM system. The specifications of the PCM system include the following: Sampling role = 8 KHz Number of representation levels = 64Determine the minimum bandwidth required if PCM wave is transmitted over a baseband channel.a)64 KHzb)32 KHzc)24 KHzd)48 KHzCorrect answer is option 'C'. Can you explain this answer?
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