Hello, I have a few questions that I need help answering concerning a baseband c

Question

Hello, I have a few questions that I need help answering concerning a baseband channel: Q: A baseband channel has a bandwidth of 10kHz. A) How do i determine the maximum symbol rate (in kbaud) if the channel is noise free? B) How do I determine the channel capacity (in kibits/s) for binary encoding if the channel is noise free? C) How do I determine the channel capacity for 16-level encoding if the channel is noise free? D) How do I determine the channel capacity for 32-level encoding if S/N ratio is 11.76 dB? E) How do I determine the channel capcity for 32-level encoding if the S/N ratio is 40 dB?

Explanation / Answer

you can get it by shanon capacity

C = B log2 [1 + (S/N)]

a)The maximum baud rate or pulse rate for a base band channel is called the Nyquist rate, and is double the bandwidth (double the cut-off frequency).

= 10* 2 K = 20 kbaud

b) assuming that 1 symbol per second so the capacity will be same as symbol rate = 20Kibits/s

c) for 16 level encoding 1 symbol = 4 bits (2^4 = 16)

so effective bitrate will be 4 times the symbol rate = 4 * 20k = 80kibits/s

d) for 32 bit encoding 1 symbol = 5 bits so bandwidth = 5 * 20K = 100kibits/s

S/N = 11.76dB taking antilog = 15

C = B log2 [1 + (S/N)] = 100k log2[1 + 15] = 400kbits/s

e) S/N = 30dB taking antilog = 1000

C = B log2 [1 + (S/N)] = 100k log2[1 + 1000] = 996.7kbits/s

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