- #1
dragonflare
- 2
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Hello all, i encountered a question which i coudnt really solve, was hoping someone could help me. Its regarding Shannons Formula for finding capacity of a channel.
So it goes like this:
C = B log (base2 ) [1 + SNR]
KEY:
C = capacity
B = bandwidth
SNR = SIgnal Noise Ratio
when the SNR (Signal Noise Ratio) is high, the above formula is not very reliable and we can use this formula instead:
*Also it states that if the SNR is high we can ignore the 1.
C = B * [SNR(subscript db)/3]
Question: How do we get the second formula after simplifying the first?-------------------------------------------------------------------------------------
This is what i have tried till now.
SNR(subscript db) = 10 log (base 10) SNR
We make SNR subject of formula :
10^(SNRdb/10) = SNR
Therefore substituting SNR in the text with the SNR (subscript dB)gives you
*We ignore the 1
C = B * log (base 2) [ 10 ^ (SNRdb / 10)]
Now I am given to understand that to find log base 2 of a number we can do this:C = [B * log (base 10) [ 10 ^ (SNRdb / 10)]] / [log (base 10) 2]
...
I am really confuse how to simplify after that.. i don't even know if I am right in the first place -.-
Any help would be appreciated.
Thanks
How do we go to this simplified formula from the one given above??
So it goes like this:
C = B log (base2 ) [1 + SNR]
KEY:
C = capacity
B = bandwidth
SNR = SIgnal Noise Ratio
when the SNR (Signal Noise Ratio) is high, the above formula is not very reliable and we can use this formula instead:
*Also it states that if the SNR is high we can ignore the 1.
C = B * [SNR(subscript db)/3]
Question: How do we get the second formula after simplifying the first?-------------------------------------------------------------------------------------
This is what i have tried till now.
SNR(subscript db) = 10 log (base 10) SNR
We make SNR subject of formula :
10^(SNRdb/10) = SNR
Therefore substituting SNR in the text with the SNR (subscript dB)gives you
*We ignore the 1
C = B * log (base 2) [ 10 ^ (SNRdb / 10)]
Now I am given to understand that to find log base 2 of a number we can do this:C = [B * log (base 10) [ 10 ^ (SNRdb / 10)]] / [log (base 10) 2]
...
I am really confuse how to simplify after that.. i don't even know if I am right in the first place -.-
Any help would be appreciated.
Thanks
How do we go to this simplified formula from the one given above??