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Sincerely, It is not my homework. It was the question asked in one German University's Online Exams.

I went through Google as well but couldn't find a single way out to figure the solution of this Problem.

A Received Signal is filtered in the low pass filter. At the Input of the Low Pass filter the Bandwidth is B=80khz and the SNR is 30 dB. What is the SNR at output of Filter if equivalent noise bandwidth of the filter (low pass filter) is 20kHz.?

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    \$\begingroup\$ The way your question is now, you are asking us to do all of the work for you. Meet us half way and tell us what you have done and what you are getting stuck at. We will then help teach you how to solve the problem. However, your question lacks some important details. What is the input signal? If the signal has a bandwidth of 80khz and you pass it through a lpf of 20 khz, then your signal wont look too good on the other end. On the other hand, if your signal is only 10 khz, a lpf will help to remove noise while keeping your signal intact. Also, what is the noise? Is it white? \$\endgroup\$ – Kellenjb Apr 4 '12 at 16:08
  • \$\begingroup\$ Sorry for the Inconvenience caused .Actually it was the question asked to me in one online exam. i went through the google and search but i couldn't figure out any relationships of SNR and the Frequency of the Signal.So i was looking for the Relationships only? \$\endgroup\$ – Bibek Apr 5 '12 at 0:54
  • \$\begingroup\$ Kellenjb is right: this question misses details. You should know the bandwith of signal and noise at least, and also the spectral distribution (if flat or whatever). Otherwise you need the SNR of the output to make the inverse process \$\endgroup\$ – clabacchio Apr 6 '12 at 7:42
  • \$\begingroup\$ Still rude to post someone's exam question. \$\endgroup\$ – Scott Seidman May 22 '13 at 10:37
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I think this is a fairly trivial question, assuming that the input signal is not filtered by the low pass filter (input signal frequency is much lower than the low pass filter bandwidth.) The reason I'm inclined to hastily jump to such assumptions is due to the format of the question, which seems to inquire if the reader is aware that noise power is the integral of noise level over the noise bandwidth of the system. Also, I think everybody reading the question would agree that it would be plainly unsolvable if these assumptions are not made.

If the case is as above, the noise power will decrease by a factor of 4, while the signal level is kept constant, and the SNR will increase to 36.02 dB at the filter output.

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  • \$\begingroup\$ Thanks for your Opinion. However up to my memory i don't think there was any Options stating 36.02 dB .Anyway i appreciate your Opinion. If you want ,please show me the Mathematical Explanation.. \$\endgroup\$ – Bibek Apr 8 '12 at 5:23
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The question makes too many assumptions. 1) THe noise is Gaussian 2) the signal is less than 20Khz 3) the LPF is of sufficient order to be considered a brick wall (steep slope) ;)

Thus the noise voltage reduces to 25% = -6db and thus SNR rises 6dB

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