# In a binary pulse code modulation system, if the frequency of the baseband signal is 12.5 kHz, then what will be the minimum transmission bandwidth of the PCM waveform if a uniform quantizer having 32 levels is used.

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In a binary pulse code modulation system, if the frequency of the baseband signal is 12.5 kHz, then what will be the minimum transmission bandwidth of the PCM waveform if a uniform quantizer having 32 levels is used.

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Calculation of the code-word length

The given problem is of binary pulse code modulation, firstly the codeword length needs to be calculated after that the required bandwidth is calculated.

The codeword length is calculated by the formula as shown below:

Q=2N

Where Q is the quantization level.

N is the codeword length.

Q=32,

Plugging the values in the above equation,

32=2N

N=5bits/word.

Calculation of the minimum transmission bandwidth

by the application of the  Shannon- Hartley theorem, for the sampling frequency, the minimum bandwidth is given by the expression as shown below for the binary pulse code modulation.

where,

N is the codeword length.

fs is the signal frequency.

B is the bandwidth

Plugging the values in the above equation,

...

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