# Signal to Noise Ratio Formula Needed.

• 06-22-2008, 09:06 PM
unix
Signal to Noise Ratio Formula Needed.

Hi,

given a known data rate in kbps and a known signal to noise ratio how
do you calculate the minimum bandwith?

thanks

Alex
• 06-22-2008, 10:31 PM
unix
Re: Signal to Noise Ratio Formula Needed.
On Jun 22, 5:06*pm, Alex <alex.co...@rbc.com> wrote:[color=blue]
> Hi,
>
> given a known data rate *in kbps and a known signal to noise ratio how
> do you calculate the minimum bandwith?
>
> thanks[/color]

You use Shannon's equation.

Capcity (b/s) = Bandwidth (Hz) * logbase2(1 + S/N)

In your case, solve for the bandwidth variable.

One important note: the term S/N is the actual signal to noise ratio,
NOT in dB, but the actual fraction of watts of signal to watts of
noise. So first, solve for that, assuming the SNR you start with is in
dB.

If you have SNR in dB going in, then S/N (power ratio) = 10 ^ (SNR(in
dB) / 10)

Also remember to use log base 2, NOT the natural log or the log base
10.

Bert
• 06-22-2008, 11:17 PM
unix
Re: Signal to Noise Ratio Formula Needed.
On Jun 22, 6:31*pm, Albert Manfredi <bert22...@hotmail.com> wrote:[color=blue]
> On Jun 22, 5:06*pm, Alex <alex.co...@rbc.com> wrote:[/color]
[color=blue][color=green]
> > given a known data rate *in kbps and a known signal to noise ratio how
> > do you calculate the minimum bandwith?[/color]
>[color=green]
> > thanks[/color]
>
> You use Shannon's equation.
>
> Capcity (b/s) = Bandwidth (Hz) * logbase2(1 + S/N)
>
> In your case, solve for the bandwidth variable.
>
> One important note: the term S/N is the actual signal to noise ratio,
> NOT in dB, but the actual fraction of watts of signal to watts of
> noise. So first, solve for that, assuming the SNR you start with is in
> dB.
>
> If you have SNR in dB going in, then S/N (power ratio) = 10 ^ (SNR(in
> dB) / 10)
>
> Also remember to use log base 2, NOT the natural log or the log base
> 10.[/color]

I should add, this is the best you can do (minimum bandwidth
required). In practice, you won't reach that value, even with good
error correction codes such as turbo codes or LDPC. But you can come
close, within, say, less than 2 dB.

Bert
• 06-23-2008, 02:04 PM
unix
Re: Signal to Noise Ratio Formula Needed.
Okay thanks for the info.

If I have for example a signal to noise ratio of 100 decibels to
convert it into watts I calculate the following first:

10 ^ (100/10)
10 ^ (10)
=10000000000 watts

Right?

then I take that value and insert it into:

Capcity (b/s) = Bandwidth (Hz) * logbase2(1 + S/N)

So If I have a capacity of 10 kbps I calculate it as the following:

10=Bandwith * logbase2(1+10000000000)
10=bandwith * logbase2(10000000001)
bandwith =10/ logbase2(10000000001)

So far correct?

Thx

Alex
On Jun 22, 7:17*pm, Albert Manfredi <bert22...@hotmail.com> wrote:[color=blue]
> On Jun 22, 6:31*pm, Albert Manfredi <bert22...@hotmail.com> wrote:
>
>
>
>
>[color=green]
> > On Jun 22, 5:06*pm, Alex <alex.co...@rbc.com> wrote:[color=darkred]
> > > given a known data rate *in kbps and a known signal to noise ratio how
> > > do you calculate the minimum bandwith?[/color][/color]
>[color=green][color=darkred]
> > > thanks[/color][/color]
>[color=green]
> > You use Shannon's equation.[/color]
>[color=green]
> > Capcity (b/s) = Bandwidth (Hz) * logbase2(1 + S/N)[/color]
>[color=green]
> > In your case, solve for the bandwidth variable.[/color]
>[color=green]
> > One important note: the term S/N is the actual signal to noise ratio,
> > NOT in dB, but the actual fraction of watts of signal to watts of
> > noise. So first, solve for that, assuming the SNR you start with is in
> > dB.[/color]
>[color=green]
> > If you have SNR in dB going in, then S/N (power ratio) = 10 ^ (SNR(in
> > dB) / 10)[/color]
>[color=green]
> > Also remember to use log base 2, NOT the natural log or the log base
> > 10.[/color]
>
> I should add, this is the best you can do (minimum bandwidth
> required). In practice, you won't reach that value, even with good
> error correction codes such as turbo codes or LDPC. But you can come
> close, within, say, less than 2 dB.
>
> Bert- Hide quoted text -
>
> - Show quoted text -[/color]

• 06-23-2008, 08:31 PM
unix
Re: Signal to Noise Ratio Formula Needed.
On Jun 23, 10:04*am, Alex <alex.co...@rbc.com> wrote:[color=blue]
> Okay thanks for the info.
>
> If I have for example a signal to noise ratio of 100 decibels to
> convert it into watts I calculate the following first:
>
> 10 ^ (100/10)
> 10 ^ (10)
> =10000000000 watts
>
> Right?
>
> then I take that value and insert it into:
>
> Capcity (b/s) = Bandwidth (Hz) * logbase2(1 + S/N)
>
> So If I have a capacity of 10 kbps I calculate it as the following:
>
> 10=Bandwith * logbase2(1+10000000000)
> 10=bandwith * logbase2(10000000001)
> bandwith =10/ logbase2(10000000001)
>
> So far correct?[/color]

Don't forget that the link capacity is in b/s, not Kb/s.

Bert
• 07-02-2008, 11:13 PM
unix
Re: Signal to Noise Ratio Formula Needed.
On Jun 23, 3:31*pm, Albert Manfredi <bert22...@hotmail.com> wrote:[color=blue]
> On Jun 23, 10:04*am, Alex <alex.co...@rbc.com> wrote:
>[color=green]
> > Okay thanks for the info.[/color]
>[color=green]
> > If I have for example a signal to noise ratio of 100 decibels to
> > convert it into watts I calculate the following first:[/color]
>[color=green]
> > 10 ^ (100/10)
> > 10 ^ (10)
> > =10000000000 watts[/color][/color]

Minor note:

SNR is a dimensionless quantity, not watts, since both numerator and
denominator are measures of power (or PSD).

-Le Chaud Lapin-