Is the below solution correct for this problem? Question:

What is the theoretical capacity of a channel in each of the following cases:

a. Bandwidth = 20 KHz SNRdB = 40

b. Bandwidth = 200 KHz SNRdB = 4

c. Bandwidth = 1 MHz SNRdB = 20

a. B=20,000 Hz

SNR(db)= 40 SNR(db) = 10* log base 10 of SNR 40 = 10 * Log base 10 of SNR Solve for SNR = 10,000 Capacity = B* Log base 2 of(1+SNR) = 20,000 * Log base 2 of(1+10,000 ) = 265,757 bits/sec

b.

B=200,000 Hz

SNR(db)= 4 SNR(db) = 10* log base 10 of SNR 4 = 10 * Log base 10 of SNR Solve for SNR = 2.511886 Capacity = B* Log base 2 of(1+SNR) = 200,000 * Log base 2 of(1+ 2.511886 ) = 362,449 bits/sec

c.

B=1 * 10^6 Hz SNR(db)= 20 SNR(db) = 10* log base 10 of SNR 20 = 10 * Log base 10 of SNR Solve for SNR = 100 Capacity = B* Log base 2 of(1+SNR) = 1 * 10^6* Log base 2 of(1+100) = 6,658,211 bits/sec