Shannon's Formula c = b log2 (1 + s)

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In summary, the conversation is about trying to understand Shannon's formula and using an example to demonstrate its correctness. The formula involves multiplying the bandwidth by the log of the signal to noise ratio plus one, and the conversation clarifies the steps involved in solving for the answer.
  • #1
Radiatedtheory18
im trying to understand shannon's formula for some time now. i have tryed to theorise if this is correct the way i have worked out an example using the formula below.

c = b x log2 (1 + s)

for example

signal to noise ratio 127
b = 3000 b = bandwidth
as shannon's formula states to add one to the signal to noise ratio to make it 128

Log 2 = 27= 128

then we multiply the log2 by the bandwidth to get

21000 Bps

C=BXL

in formula the answer

21000 = 3000 x log2

is that correct?
 
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  • #2
You get the right answer, but your presentation is confusing. You should state clearly that the log of 128 to the base 2 is 7, and then show the multiplication of that 7 by 3000 to give the answer 21000.

The way you have it now gives a first impression of being wrong.
 
  • #3
128 = log to the base 2 is 27

7 x 3000 = 21000bps
 

FAQ: Shannon's Formula c = b log2 (1 + s)

What is Shannon's Formula and what does it represent?

Shannon's Formula, also known as the Shannon-Hartley Theorem, is a mathematical formula developed by Claude Shannon in 1948. It is used to calculate the maximum rate at which data can be transmitted over a communication channel with a specific bandwidth and signal-to-noise ratio.

How is Shannon's Formula used in communication systems?

Shannon's Formula is used in communication systems to determine the maximum amount of information that can be transmitted over a channel without errors. It helps in designing efficient communication systems by providing a theoretical upper limit on the data rate.

What do the variables in Shannon's Formula represent?

The variable c represents the channel capacity, which is the maximum rate of information that can be transmitted. The variable b represents the bandwidth of the channel, and s represents the signal-to-noise ratio, which is the ratio of the signal power to the noise power in the channel.

Can Shannon's Formula be applied to all communication channels?

Yes, Shannon's Formula can be applied to all communication channels, including wireless, optical, and wired channels. However, it assumes that the channel is linear, time-invariant, and additive white Gaussian noise (AWGN) channel.

How is Shannon's Formula related to the concept of data compression?

Shannon's Formula is closely related to the concept of data compression. It states that the maximum data rate is directly proportional to the bandwidth and the logarithm of the signal-to-noise ratio. This means that by increasing the signal-to-noise ratio or the bandwidth, the data rate can be increased. However, this also implies that by compressing the data, the bandwidth required to transmit it can be reduced, thus increasing the data rate.

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