# Bandpass signal sampling

Started by February 10, 2008
```Hi,

I have a problem.
If anyone may help , I would be appreciated.

There are signals at 70 MHz IF output of a DDC.
and there are equispace signals which should be demodulated.
I am trying to find the best sampling frequency for this purpose.

I know about the bandpass sampling theorem which says:

Fs >= 2*B (1)

(2Fc-B)/m >= fs >= (2*Fc + B)/(m+1) (2)

Where Fs = Sampling frequency
Fc = Center Frequency
B = Bandwidth
M any integer which satisfies the condition (1)

But that is for one signal which is at Fc with BW = B

But what about many signals around the Signal of Interest ?

If you could not find the correct Fs, There may occur aliasing between the
other signals as well.

```
```"Dedicated" <dedicated_glory@hotmail.com> wrote in message
news:xI-dnYOHL5K8EzLanZ2dnUVZ_rOqnZ2d@giganews.com...
> Hi,
>
> I have a problem.
> If anyone may help , I would be appreciated.
>
> There are signals at 70 MHz IF output of a DDC.
> and there are equispace signals which should be demodulated.
> I am trying to find the best sampling frequency for this purpose.
>
> I know about the bandpass sampling theorem which says:
>
> Fs >= 2*B (1)
>
> (2Fc-B)/m >= fs >= (2*Fc + B)/(m+1) (2)
>
> Where Fs = Sampling frequency
> Fc = Center Frequency
> B = Bandwidth
> M any integer which satisfies the condition (1)
>
>
> But that is for one signal which is at Fc with BW = B
>
> But what about many signals around the Signal of Interest ?
>
> If you could not find the correct Fs, There may occur aliasing between the
> other signals as well.

Just change the bandwidth to the *total* bandwidth of all signals of
interest.

Fred

```
```On 11 Feb, 03:40, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:
> "Dedicated" <dedicated_gl...@hotmail.com> wrote in message
>
> news:xI-dnYOHL5K8EzLanZ2dnUVZ_rOqnZ2d@giganews.com...
>
>
>
>
>
> > Hi,
>
> > I have a problem.
> > If anyone may help , I would be appreciated.
>
> > There are signals at 70 MHz IF output of a DDC.
> > and there are equispace signals which should be demodulated.
> > I am trying to find the best sampling frequency for this purpose.
>
> > I know about the bandpass sampling theorem which says:
>
> > Fs >= 2*B (1)
>
> > (2Fc-B)/m >= fs >= (2*Fc + B)/(m+1) (2)
>
> > Where Fs = Sampling frequency
> > Fc = Center Frequency
> > B = Bandwidth
> > M any integer which satisfies the condition (1)
>
> > But that is for one signal which is at Fc with BW = B
>
> > But what about many signals around the Signal of Interest ?
>
> > If you could not find the correct Fs, There may occur aliasing between the
> > other signals as well.
>
> Just change the bandwidth to the *total* bandwidth of all signals of
> interest.

...or demodulate before sampling.

Rune
```
```Dedicated wrote:
> Hi,
>
> I have a problem.
> If anyone may help , I would be appreciated.
>
> There are signals at 70 MHz IF output of a DDC.
> and there are equispace signals which should be demodulated.
> I am trying to find the best sampling frequency for this purpose.
>
> I know about the bandpass sampling theorem which says:
>
> Fs >= 2*B (1)
>
> (2Fc-B)/m >= fs >= (2*Fc + B)/(m+1) (2)
>
> Where Fs = Sampling frequency
> Fc = Center Frequency
> B = Bandwidth
> M any integer which satisfies the condition (1)
>
>
> But that is for one signal which is at Fc with BW = B
>
> But what about many signals around the Signal of Interest ?
>
> If you could not find the correct Fs, There may occur aliasing between the
> other signals as well.

I'm trying to sort out what you mean, and I'm not getting it.

I _can_ tell that you are trying to go beyond a rule without
understanding the reasoning behind it.  When you find yourself doing
this, the best thing to do is to study the rule, understand what goes
help, in a tangential way:
http://www.wescottdesign.com/articles/Sampling/sampling.html.

It seems that you want to sample a signal and interference without
filtering out the interference before sampling, and you want to know how
fast to sample?  If that's the case then take Fred's advise -- or do
some filtering before you hit your sampler.

When I hit a problem like this I make sure to make a little diagram,
like the ones you see in textbooks, that show the spectrum of the signal
before sampling, all the folding frequencies due to sampling, then a
separate sketch of the signal (fortuitously sampled to within my
sampling rate, I hope) and all of it's aliases (which don't interfere
with the part of the signal that I want, I hope).  This aids in my
understanding, so I have confidence I'm not blindly (and possibly
incorrectly) applying a rule that I don't understand.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html
```
```"Tim Wescott" <tim@seemywebsite.com> wrote in message
news:nuydnfRdPIqYEy3anZ2dnUVZ_qOknZ2d@web-ster.com...
> Dedicated wrote:
>> Hi,
>>
>> I have a problem.
>> If anyone may help , I would be appreciated.
>>
>> There are signals at 70 MHz IF output of a DDC.
>> and there are equispace signals which should be demodulated.
>> I am trying to find the best sampling frequency for this purpose.
>>
>> I know about the bandpass sampling theorem which says:
>>
>> Fs >= 2*B (1)
>>
>> (2Fc-B)/m >= fs >= (2*Fc + B)/(m+1) (2)
>>
>> Where Fs = Sampling frequency
>> Fc = Center Frequency B = Bandwidth
>> M any integer which satisfies the condition (1)
>>
>>
>> But that is for one signal which is at Fc with BW = B
>>
>> But what about many signals around the Signal of Interest ?
>>
>> If you could not find the correct Fs, There may occur aliasing between
>> the
>> other signals as well.
>
> I'm trying to sort out what you mean, and I'm not getting it.
>
> I _can_ tell that you are trying to go beyond a rule without understanding
> the reasoning behind it.  When you find yourself doing this, the best
> thing to do is to study the rule, understand what goes into it, then take
> way: http://www.wescottdesign.com/articles/Sampling/sampling.html.
>
> It seems that you want to sample a signal and interference without
> filtering out the interference before sampling, and you want to know how
> fast to sample?  If that's the case then take Fred's advise -- or do some
> filtering before you hit your sampler.
>
> When I hit a problem like this I make sure to make a little diagram, like
> the ones you see in textbooks, that show the spectrum of the signal before
> sampling, all the folding frequencies due to sampling, then a separate
> sketch of the signal (fortuitously sampled to within my sampling rate, I
> hope) and all of it's aliases (which don't interfere with the part of the
> signal that I want, I hope).  This aids in my understanding, so I have
> confidence I'm not blindly (and possibly incorrectly) applying a rule that
> I don't understand.
>
> --
>
> Tim Wescott
> Wescott Design Services
> http://www.wescottdesign.com
>

I sure agree with the diagrams ... I call 'em "cartoons".

Fred

```