# nyquist sampling rate

Started by May 5, 2009
```hi all.
i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
the Nyquist sampling rate is (5+2/2)*2 = 12 MHz. But I have heard that
it is not a good idea to sample on or near nyquist rate because of the
oversample it a little such as 16 or 20 MHz. I am working on a
communication system so the system is performance limited.

Thanks
```
```<aitezaz.abd@gmail.com> wrote in message
> i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
> the Nyquist sampling rate is (5+2/2)*2 = 12 MHz.

If BW is 2 then Nyquist Rate is 4.

This is because you are interested only in reproducing the shape
of your original signal and have no interest in the shape of
the 5MHz carrier wave.

```
```On May 5, 2:43&#2013266080;pm, "Alun" <no.spam.thank....@invalid.invalid> wrote:
> <aitezaz....@gmail.com> wrote in message
>
>
> > i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
> > the Nyquist sampling rate is (5+2/2)*2 = 12 MHz.
>
> If BW is 2 then Nyquist Rate is 4.
>
> This is because you are interested only in reproducing the shape
> of your original signal and have no interest in the shape of
> the 5MHz carrier wave.

yes you are right. but i want to understand this thing in general for
nyquist sampling instead of bandpass sampling. i.e. consider 8 MHz of
bandwidth with 5 MHz carrier. Now i cannot use 16 MHz as sampling rate
because it will cause overlapping of the spectra. Please guide me for
the case when i am nyquist sampling the signal i.e. (5+4)x2=18 MHz. I
put my question again as follows.

Is it OK to sample at nyquist rate (2xmaximum frequency present in
signal) considering the sinx/x roll of characteristics of ADC or
should i  oversample it a little bit. Or put it another way... is it
OK to have your spectrum tightly packed between -Fs/2 to Fs/2 ? (as in
this case the frequencies near the Fs/2 and -Fs/2 would suffer a loss
because of sinx/x characteristics.)

```
```<aitezaz.abd@gmail.com> wrote in message
> hi all.
> i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
> the Nyquist sampling rate is (5+2/2)*2 = 12 MHz. But I have heard that
> it is not a good idea to sample on or near nyquist rate because of the
> oversample it a little such as 16 or 20 MHz. I am working on a
> communication system so the system is performance limited.
>
> Thanks

```
```On May 5, 6:01 am, aitezaz....@gmail.com wrote:
> On May 5, 2:43 pm, "Alun" <no.spam.thank....@invalid.invalid> wrote:
>
> > <aitezaz....@gmail.com> wrote in message
>
>
> > > i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
> > > the Nyquist sampling rate is (5+2/2)*2 = 12 MHz.
>
> > If BW is 2 then Nyquist Rate is 4.
>
> > This is because you are interested only in reproducing the shape
> > of your original signal and have no interest in the shape of
> > the 5MHz carrier wave.
>
> yes you are right. but i want to understand this thing in general for
> nyquist sampling instead of bandpass sampling. i.e. consider 8 MHz of
> bandwidth with 5 MHz carrier. Now i cannot use 16 MHz as sampling rate
> because it will cause overlapping of the spectra. Please guide me for
> the case when i am nyquist sampling the signal i.e. (5+4)x2=18 MHz. I
> put my question again as follows.
>
> Is it OK to sample at nyquist rate (2xmaximum frequency present in
> signal) considering the sinx/x roll of characteristics of ADC or
> should i  oversample it a little bit. Or put it another way... is it
> OK to have your spectrum tightly packed between -Fs/2 to Fs/2 ? (as in
> this case the frequencies near the Fs/2 and -Fs/2 would suffer a loss
> because of sinx/x characteristics.)
>

Talking about the spectum being between -Fs/2 to Fs/2 implies that you
are using quadrature sampling.  With real sampling you need to limit
the signal bandwidth to 0 to Fs/2 to prevent aliasing.

When you talk about "sinx/x roll of charactersistics of ADC" I'm not
sure this is exactly the right way to put it.  The problem with sample
rate is aliasing and filtering.  If your signal is bandwidth limited
to 0 to Fs/2, then the sampled version will be accurate with no
aliasing.  In the real world, filters are not perfect and a design
needs to allow for a transition band in the filter.  So it works
better to use perhaps 80% ro 90% of the available bandwidth for your
signal.

In your example with a 5 MHz carrier and a 2 MHz wide signal, you
would do well to sample around 15 MHz or higher.  If you sample at 4
MHz, the real signal would alias down to 0 to 2 MHz, however this does
not allow for the transition band of a real design.  Another choice
might be to sample at 7 MHz bringing the signal to 1 to 3 MHz region.
But this presents an inverted spectrum which may or may not be an
issue for your application.  Sampling above 12 MHz will give you a
spectrum that is entirely within the Nyquist bandwidth is not
inverted.

If the signal bandwidth were not so wide, say 1 MHz, you could sub-
sample at a rate just below the low end of the lowest frequency, say 4
MHz, to shift the band near 0 Hz and retain a non-inverted spectrum.
In this example the resulting spectrum would be between 0.5 and 1.5
MHz with a 2 MHz Nyquist rate.  This would allow a reasonably wide
transition band on your anti-alias filter.

Rick
```
```"Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message
news:0LULl.17832\$D32.1661@flpi146.ffdc.sbc.com...
>
> <aitezaz.abd@gmail.com> wrote in message
>> hi all.
>> i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
>> the Nyquist sampling rate is (5+2/2)*2 = 12 MHz. But I have heard that
>> it is not a good idea to sample on or near nyquist rate because of the
>> oversample it a little such as 16 or 20 MHz. I am working on a
>> communication system so the system is performance limited.
>>
>> Thanks

Is that you're latest 'clever' word Vlad? Are you four?

```
```On May 5, 5:43&#2013266080;am, "Alun" <no.spam.thank....@invalid.invalid> wrote:
> <aitezaz....@gmail.com> wrote in message
>
>
> > i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
> > the Nyquist sampling rate is (5+2/2)*2 = 12 MHz.
>
> If BW is 2 then Nyquist Rate is 4.
>
> This is because you are interested only in reproducing the shape
> of your original signal and have no interest in the shape of
> the 5MHz carrier wave.

If sampled after demodulation. Otherwise the result will be aliased.

Hope this helps.

Greg
```
```On Tue, 05 May 2009 00:29:59 -0700, aitezaz.abd wrote:

> hi all.
> i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means the
> Nyquist sampling rate is (5+2/2)*2 = 12 MHz. But I have heard that it is
> not a good idea to sample on or near nyquist rate because of the sinx/x
> roll of charactersistics of ADC. Please guide should i oversample it a
> little such as 16 or 20 MHz. I am working on a communication system so
> the system is performance limited.
>
> Thanks

Nyquist didn't say that:
http://www.wescottdesign.com/articles/Sampling/sampling.html.

--
http://www.wescottdesign.com
```
```On 2009-05-05, aitezaz.abd@gmail.com <aitezaz.abd@gmail.com> wrote:
> i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
> the Nyquist sampling rate is (5+2/2)*2 = 12 MHz. But I have heard that
> it is not a good idea to sample on or near nyquist rate

I asked a very similar question a while ago, only in the context of a
DAC.  In the same way that you quickly rejected "4MHz" as your sampling
rate because your data is not perfectly bandpass filtered you can reject
12MHz because your data is not perfectly lowpass filtered.  Whatever
analog filter you have on your input has a transition band.  Wherever
the rolloff of that filter crosses the limit of your tolerance for
aliasing is the true bandwidth of your input (it's a little more tricky
than that because the first bit of noise above Nyquist folds back onto
the extra bit of sampling bandwidth you don't care about anyway).

--
<ben@ben.com>
http://www.ben.com/
```
```On May 6, 5:41&#2013266080;am, Ben Jackson <b...@ben.com> wrote:
> On 2009-05-05, aitezaz....@gmail.com <aitezaz....@gmail.com> wrote:
>
> > i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
> > the Nyquist sampling rate is (5+2/2)*2 = 12 MHz. But I have heard that
> > it is not a good idea to sample on or near nyquist rate
>
> I asked a very similar question a while ago, only in the context of a
> DAC. &#2013266080;In the same way that you quickly rejected "4MHz" as your sampling
> rate because your data is not perfectly bandpass filtered you can reject
> 12MHz because your data is not perfectly lowpass filtered. &#2013266080;Whatever
> analog filter you have on your input has a transition band. &#2013266080;Wherever
> the rolloff of that filter crosses the limit of your tolerance for
> aliasing is the true bandwidth of your input (it's a little more tricky
> than that because the first bit of noise above Nyquist folds back onto
> the extra bit of sampling bandwidth you don't care about anyway).
>
> --
> <b...@ben.com>http://www.ben.com/

Thanks for replies guys.
Yes Ben you got it right and I have found the same answer on
http://www.dspdesignline.com/howto/207500439
We cannot sample the signal on twice the maximum frequency present in
the signal because in this case the anti aliasing filter would be
impossible to realize. Instead, we should sample it at twice the ws
where ws is the starting frequency of stop band.
Now, the next question that i would like to ask is how much
oversampled a signal should be (as a rule of thumb) so that we can
make practically feasible anti aliasing filters(subject to current
technology of analog filters).