# Calculate variance of noise

Started by July 2, 2008
```HI All

I really need your help to understand this noise concept.

Can you please tell me how to calculate noise variance for bandpass
simulation?

And does oversampling affects noise variance calculation.

Your help will be greatly appreciated.

Thanks

Chintan
```
```>Can you please tell me how to calculate noise variance for bandpass
>simulation?
If you know the variance of the signal in the band, you can simply
calculate the sample variance (sum of the squares of N data points divided
by N-1) of the aggregate and subtract the known signal variance.

>And does oversampling affects noise variance calculation.
No.

Mark
```
```>>Can you please tell me how to calculate noise variance for bandpass
>>simulation?
>If you know the variance of the signal in the band, you can simply
>calculate the sample variance (sum of the squares of N data points
divided
>by N-1) of the aggregate and subtract the known signal variance.
>
>>And does oversampling affects noise variance calculation.
>No.
>
>Mark
>
%%%%

HI

Thanks a lot Mark.

Now my signal is band limited to 8 KHz, convolutionaly coded and QPSK
modulation, fs=48KHz.

My problem is to add white noise to this signal. Please check my steps:

EbNO_dB=0:5;
EbNO=10.^(EbNO-dB/10);

M=4;    % QPSK
Es=1;   % Average Symbol Energy

Rc=1/2; % code rate

sigma=sqrt(Es/(2*Rc*log2(M)*EbNO));

y=x+sigma*randn(size(x));

where x is bandlimted real signal.

Please just tell me if this steps are correct.

Thanks

Chintan

```
```On Jul 2, 11:25 am, "markt" <tak...@pericle.com> wrote:
> >Can you please tell me how to calculate noise variance for bandpass
> >simulation?
>
> If you know the variance of the signal in the band, you can simply
> calculate the sample variance (sum of the squares of N data points divided
> by N-1) of the aggregate and subtract the known signal variance.
>
> >And does oversampling affects noise variance calculation.
>
> No.
>
> Mark

If the noise is colored, which happens when its oversampled, it
certainly does affect the variance calculation.
```
```>On Jul 2, 11:25 am, "markt" <tak...@pericle.com> wrote:
>> >Can you please tell me how to calculate noise variance for bandpass
>> >simulation?
>>
>> If you know the variance of the signal in the band, you can simply
>> calculate the sample variance (sum of the squares of N data points
divided
>> by N-1) of the aggregate and subtract the known signal variance.
>>
>> >And does oversampling affects noise variance calculation.
>>
>> No.
>>
>> Mark
>
>If the noise is colored, which happens when its oversampled, it
>certainly does affect the variance calculation.
>

Hi

So can you please give some sort of formula to calculate sigma.?

I have tried almost all the books but I am not getting anything.

Chintan
```
```On Jul 3, 4:40 am, "cpshah99" <cpsha...@rediffmail.com> wrote:
> >On Jul 2, 11:25 am, "markt" <tak...@pericle.com> wrote:
> >> >Can you please tell me how to calculate noise variance for bandpass
> >> >simulation?
>
> >> If you know the variance of the signal in the band, you can simply
> >> calculate the sample variance (sum of the squares of N data points
> divided
> >> by N-1) of the aggregate and subtract the known signal variance.
>
> >> >And does oversampling affects noise variance calculation.
>
> >> No.
>
> >> Mark
>
> >If the noise is colored, which happens when its oversampled, it
> >certainly does affect the variance calculation.
>
> Hi
>
> So can you please give some sort of formula to calculate sigma.?
>
> I have tried almost all the books but I am not getting anything.
>
>
> Chintan

When you oversample, you don't increase the number of "Degrees of
Freedom". Essentially oversampled white noise is not white.  I have a
book on SONAR by Neilson that I don't have handy so I'm going off
memory.  You can do some experiments in Matlab to check it out.  If
you oversample by 2, and you have 2N samples, sum the squares, but
divide by N, not 2N.

```
```On Jul 4, 2:13 am, stanp <stan.p...@gmail.com> wrote:
> On Jul 3, 4:40 am, "cpshah99" <cpsha...@rediffmail.com> wrote:
>
>
>
> > >On Jul 2, 11:25 am, "markt" <tak...@pericle.com> wrote:
> > >> >Can you please tell me how to calculate noise variance for bandpass
> > >> >simulation?
>
> > >> If you know the variance of the signal in the band, you can simply
> > >> calculate the sample variance (sum of the squares of N data points
> > divided
> > >> by N-1) of the aggregate and subtract the known signal variance.
>
> > >> >And does oversampling affects noise variance calculation.
>
> > >> No.
>
> > >> Mark
>
> > >If the noise is colored, which happens when its oversampled, it
> > >certainly does affect the variance calculation.
>
> > Hi
>
> > So can you please give some sort of formula to calculate sigma.?
>
> > I have tried almost all the books but I am not getting anything.
>
>
> > Chintan
>
> When you oversample, you don't increase the number of "Degrees of
> Freedom". Essentially oversampled white noise is not white.  I have a
> book on SONAR by Neilson that I don't have handy so I'm going off
> memory.  You can do some experiments in Matlab to check it out.  If
> you oversample by 2, and you have 2N samples, sum the squares, but
> divide by N, not 2N.

Or you can calculate the variance recursively and you don't need N at