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From: Greg Heath on 26 Jan 2010 23:11
On Jan 26, 8:50 pm, "chengnoon" <chengn...(a)gmail.com> wrote:
> >The correct expression for SNR would normalize the denominator by the
> >number of bins.
>
> >So,
> >SNR =3D 10*log10((N_FFT-1)*|disired single bin magnitude|^2/sum(|all
> >bins magnitude other than desired|^2))
>
> >Regards,
> >Dilip.
>
> May be I am not present the question clearly.
> Regardless of the fft lenght difference, the ratio
> |desired signal single bin magnitude|/|any other signal single bin
> magnitude|
> is a constant.
>
> So, the SNR calculation should be like this:
> SNR = 10*log10(A)
>
> where, A = M_sig/(M_1+M_2+M_3+...+M_N)
> and N is the fft length.
>
> As the fact that M_sig/M_n is a constant regardless of the fft length N.
>
> So, we get the SNR which depends on the fft length N, i.e., the longer fft
> length, the worse SNR.
>
> This is question.
>
> Thanks a lot.

No.

You have to use the ratio of the average signal power to the average
noise power. The average noise power is relatively independent of N.

Hope this helps.

Greg
From: chengnoon on 27 Jan 2010 00:22

>
>No.
>
>You have to use the ratio of the average signal power to the average
>noise power. The average noise power is relatively independent of N.
>
>Hope this helps.
>
>Greg
>

I donot think so. SNR is defined as the ratio of a signal power to the
noise power corrupting the signal. And, the noise power is refer to the
total noise power, not the average noise power, in desired bandwidth.
From: Jerry Avins on 27 Jan 2010 00:35
chengnoon wrote:
>> No.
>>
>> You have to use the ratio of the average signal power to the average
>> noise power. The average noise power is relatively independent of N.
>>
>> Hope this helps.
>>
>> Greg
>>
>
> I donot think so. SNR is defined as the ratio of a signal power to the
> noise power corrupting the signal. And, the noise power is refer to the
> total noise power, not the average noise power, in desired bandwidth.

I think you misunderstand, probably because the explanation wasn't
complete enough. The bins have dimension. The area is amplitude times
bandwidth. As more FFT points are added, the bandwidth of a bin
decreases. The bin power is bin amplitude times bin bandwidth. The total
noise power is noise amplitude times total bandwidth. The total
bandwidth is independent of number of bins. Can you take it from here?

Jerry
--
Engineering is the art of making what you want from things you can get.
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From: chengnoon on 27 Jan 2010 01:11
>chengnoon wrote:
>>> No.
>>>
>>> You have to use the ratio of the average signal power to the average
>>> noise power. The average noise power is relatively independent of N.
>>>
>>> Hope this helps.
>>>
>>> Greg
>>>
>>
>> I donot think so. SNR is defined as the ratio of a signal power to the
>> noise power corrupting the signal. And, the noise power is refer to
the
>> total noise power, not the average noise power, in desired bandwidth.
>
>I think you misunderstand, probably because the explanation wasn't
>complete enough. The bins have dimension. The area is amplitude times
>bandwidth. As more FFT points are added, the bandwidth of a bin
>decreases. The bin power is bin amplitude times bin bandwidth. The total

>noise power is noise amplitude times total bandwidth. The total
>bandwidth is independent of number of bins. Can you take it from here?
>
>Jerry


But the signal considered here is the ideal single tone frequency, for
example single frequency signal A*cos(2*pi*fc), and it only have one single
bin regardless the fft length.

Thanks.

From: glen herrmannsfeldt on 27 Jan 2010 01:43
Jerry Avins <jya(a)ieee.org> wrote:
(snip)

> I think you misunderstand, probably because the explanation wasn't
> complete enough. The bins have dimension. The area is amplitude times
> bandwidth. As more FFT points are added, the bandwidth of a bin
> decreases. The bin power is bin amplitude times bin bandwidth. The total
> noise power is noise amplitude times total bandwidth. The total
> bandwidth is independent of number of bins. Can you take it from here?

Well, for a truly periodic signal (unlikely in this case) the
bins are delta functions. They still have area, though.
(Zero width and finite area.) For non-periodic signals you
approximate the bins as a histogram would come out.

-- glen
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