Undersampling Question

Started by June 7, 2005
```Dear folks,

I was wondering if you could help me with this problem. I have an
accelerometer with a resonance of say 15kHz. I need to do envelope
detection of this (acts a bit like AM with 15kHz as the 'carrier'). The
bandwidth of this signal is lets say 4kHz so that we bandlimit from
13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume
I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this
right? Do I then need to bandlimit the undersampled signal or will this
do the trick or what must I sample at? Also, the accelerometer has a
natural resonance and hence do I need to bandlimit before sampling ie
can I use the natural filtering roll-off of the transducer?

Thanks

```
```My calculations show that 8kHz sampling would be a bad choice. Two of your
images would overlap and would end up causing you grief. A sample rate of
10kHz  will perfectly straddle the images and ensure that the sidebands of
the images do not overlap.

Thomas

<sheepshaggerx@yahoo.co.uk> wrote in message
> Dear folks,
>
> I was wondering if you could help me with this problem. I have an
> accelerometer with a resonance of say 15kHz. I need to do envelope
> detection of this (acts a bit like AM with 15kHz as the 'carrier'). The
> bandwidth of this signal is lets say 4kHz so that we bandlimit from
> 13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume
> I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this
> right? Do I then need to bandlimit the undersampled signal or will this
> do the trick or what must I sample at? Also, the accelerometer has a
> natural resonance and hence do I need to bandlimit before sampling ie
> can I use the natural filtering roll-off of the transducer?
>
>
> Thanks
>

```
```8 KHz is in any case too slow. The sample rate must exceed twice the
bandwidth if there is to be any hope of building practical filters.

Doesn't top posting really chop up a message?

Jerry

Thomas Magma wrote:
> My calculations show that 8kHz sampling would be a bad choice. Two of your
> images would overlap and would end up causing you grief. A sample rate of
> 10kHz  will perfectly straddle the images and ensure that the sidebands of
> the images do not overlap.
>
> Thomas
>
> <sheepshaggerx@yahoo.co.uk> wrote in message
>
>>Dear folks,
>>
>>I was wondering if you could help me with this problem. I have an
>>accelerometer with a resonance of say 15kHz. I need to do envelope
>>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The
>>bandwidth of this signal is lets say 4kHz so that we bandlimit from
>>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume
>>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this
>>right? Do I then need to bandlimit the undersampled signal or will this
>>do the trick or what must I sample at? Also, the accelerometer has a
>>natural resonance and hence do I need to bandlimit before sampling ie
>>can I use the natural filtering roll-off of the transducer?
>>
>>
>>Thanks
>>
>
>
>

--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```On Tue, 07 Jun 2005 23:11:30 -0400, Jerry Avins <jya@ieee.org> wrote:

>Doesn't top posting really chop up a message?
>
>Jerry

That seems to be a matter of personal preference, but enough so that
some folks seem to get religious about it.

We've been doing this long enough that for me it makes no difference
whether people are top posting or bottom posting - I can work with
either equally well.   Mixing them in a response can be problematic,
though...  ;)

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org
```
```On 7 Jun 2005 15:09:14 -0700, sheepshaggerx@yahoo.co.uk wrote:

>Dear folks,
>
>I was wondering if you could help me with this problem. I have an
>accelerometer with a resonance of say 15kHz. I need to do envelope
>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The
>bandwidth of this signal is lets say 4kHz so that we bandlimit from
>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume
>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this
>right? Do I then need to bandlimit the undersampled signal or will this
>do the trick or what must I sample at? Also, the accelerometer has a
>natural resonance and hence do I need to bandlimit before sampling ie
>can I use the natural filtering roll-off of the transducer?
>
>
>Thanks

Hi Sheepshagger,

as Thomas said, an 8 kHz sample rate will
not work.  If your analog signal is *perfectly*
bandlimited to 4 kHz, the acceptable sample rates
are in the following ranges (kHz):

Fs_ranges =

17.0       -to-  26.0
11.333333  -to-  13.0
8.5       -to-  8.666666

Choosing an acceptable sample rate depends on the
shape of the spectrum of your analog signal.
Does your signal's 4 kHz-wide spectrum look like:

|<-- 4 kHz  -->|
****************
*              *
*              *
*              *
*              *
*              *
*                *
*                  *
-------------------------------->  Freq

or does it look like the following

|<-- 4 kHz  -->|
****************
*                *
*                  *
*                    *
*                      *
*                        *
*                          *
*                            *
--------------------------------------->  Freq

The answer to the above question makes all the difference
in the world when it comes to selecting an acceptable
bandpass sample rate.

See Ya',
[-Rick-]

```
```Eric Jacobsen wrote:
> On Tue, 07 Jun 2005 23:11:30 -0400, Jerry Avins <jya@ieee.org> wrote:
>
>
>>Doesn't top posting really chop up a message?
>>
>>Jerry
>
>
> That seems to be a matter of personal preference, but enough so that
> some folks seem to get religious about it.
>
> We've been doing this long enough that for me it makes no difference
> whether people are top posting or bottom posting - I can work with
> either equally well.   Mixing them in a response can be problematic,
> though...  ;)

That's why I didn't mix. Note that my news writer puts my sig at the bottom.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```"Jerry Avins" <jya@ieee.org> wrote in message
>8 KHz is in any case too slow. The sample rate must exceed twice the
>bandwidth if there is to be any hope of building practical filters.
>
> Doesn't top posting really chop up a message?
>
> Jerry
>
> Thomas Magma wrote:
>> My calculations show that 8kHz sampling would be a bad choice. Two of
>> your images would overlap and would end up causing you grief. A sample
>> rate of 10kHz  will perfectly straddle the images and ensure that the
>> sidebands of the images do not overlap.
>>
>> Thomas
>>
>> <sheepshaggerx@yahoo.co.uk> wrote in message
>>
>>>Dear folks,
>>>
>>>I was wondering if you could help me with this problem. I have an
>>>accelerometer with a resonance of say 15kHz. I need to do envelope
>>>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The
>>>bandwidth of this signal is lets say 4kHz so that we bandlimit from
>>>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume
>>>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this
>>>right? Do I then need to bandlimit the undersampled signal or will this
>>>do the trick or what must I sample at? Also, the accelerometer has a
>>>natural resonance and hence do I need to bandlimit before sampling ie
>>>can I use the natural filtering roll-off of the transducer?
>>>
>>>
>>>Thanks
>>>
>>
>>
>>
>
>
> --
> Engineering is the art of making what you want from things you can get.
> &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;

```
```>> Doesn't top posting really chop up a message?
>>

As I was trying to say....until the news reader's (OE) little reply button
defaults to bottom posting, that's what I'm sticking with.

Talk to Gates.

"Thomas Magma" <somewhere@overtherainbow.com> wrote in message
news:slEpe.1599395\$Xk.97455@pd7tw3no...
>
> "Jerry Avins" <jya@ieee.org> wrote in message
>>8 KHz is in any case too slow. The sample rate must exceed twice the
>>bandwidth if there is to be any hope of building practical filters.
>>
>> Doesn't top posting really chop up a message?
>>
>> Jerry
>>
>> Thomas Magma wrote:
>>> My calculations show that 8kHz sampling would be a bad choice. Two of
>>> your images would overlap and would end up causing you grief. A sample
>>> rate of 10kHz  will perfectly straddle the images and ensure that the
>>> sidebands of the images do not overlap.
>>>
>>> Thomas
>>>
>>> <sheepshaggerx@yahoo.co.uk> wrote in message
>>>
>>>>Dear folks,
>>>>
>>>>I was wondering if you could help me with this problem. I have an
>>>>accelerometer with a resonance of say 15kHz. I need to do envelope
>>>>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The
>>>>bandwidth of this signal is lets say 4kHz so that we bandlimit from
>>>>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume
>>>>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this
>>>>right? Do I then need to bandlimit the undersampled signal or will this
>>>>do the trick or what must I sample at? Also, the accelerometer has a
>>>>natural resonance and hence do I need to bandlimit before sampling ie
>>>>can I use the natural filtering roll-off of the transducer?
>>>>
>>>>
>>>>Thanks
>>>>
>>>
>>>
>>>
>>
>>
>> --
>> Engineering is the art of making what you want from things you can get.
>> &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
>
>

```
```> Fs_ranges =
>
>   17.0       -to-  26.0
>   11.333333  -to-  13.0
>    8.5       -to-  8.666666

Hi Rick,

Are you saying that my suggested 10 kHz sample rate would not work? (I
understand that I might have done the math wrong.)

Cheers,
Thomas

"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> wrote in message
news:42a6def5.1763256125@news.sf.sbcglobal.net...
> On 7 Jun 2005 15:09:14 -0700, sheepshaggerx@yahoo.co.uk wrote:
>
>>Dear folks,
>>
>>I was wondering if you could help me with this problem. I have an
>>accelerometer with a resonance of say 15kHz. I need to do envelope
>>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The
>>bandwidth of this signal is lets say 4kHz so that we bandlimit from
>>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume
>>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this
>>right? Do I then need to bandlimit the undersampled signal or will this
>>do the trick or what must I sample at? Also, the accelerometer has a
>>natural resonance and hence do I need to bandlimit before sampling ie
>>can I use the natural filtering roll-off of the transducer?
>>
>>
>>Thanks
>
>
> Hi Sheepshagger,
>
>  as Thomas said, an 8 kHz sample rate will
> not work.  If your analog signal is *perfectly*
> bandlimited to 4 kHz, the acceptable sample rates
> are in the following ranges (kHz):
>
> Fs_ranges =
>
>   17.0       -to-  26.0
>   11.333333  -to-  13.0
>    8.5       -to-  8.666666
>
>
> Choosing an acceptable sample rate depends on the
> shape of the spectrum of your analog signal.
> Does your signal's 4 kHz-wide spectrum look like:
>
>
>            |<-- 4 kHz  -->|
>            ****************
>            *              *
>            *              *
>            *              *
>            *              *
>            *              *
>           *                *
>          *                  *
>     -------------------------------->  Freq
>
> or does it look like the following
>
>
>
>            |<-- 4 kHz  -->|
>            ****************
>           *                *
>          *                  *
>         *                    *
>        *                      *
>       *                        *
>      *                          *
>     *                            *
> --------------------------------------->  Freq
>
> The answer to the above question makes all the difference
> in the world when it comes to selecting an acceptable
> bandpass sample rate.
>
> See Ya',
> [-Rick-]
>

```
```"Jerry Avins" <jya@ieee.org> wrote in message
news:69idnaPjoOsYajvfRVn-3g@rcn.net...
> Eric Jacobsen wrote:
> > On Tue, 07 Jun 2005 23:11:30 -0400, Jerry Avins <jya@ieee.org> wrote:
> >
> >
> >>Doesn't top posting really chop up a message?
> >>
> >>Jerry
> >
> >
> > That seems to be a matter of personal preference, but enough so that
> > some folks seem to get religious about it.
> >
> > We've been doing this long enough that for me it makes no difference
> > whether people are top posting or bottom posting - I can work with
> > either equally well.   Mixing them in a response can be problematic,
> > though...  ;)
>
> That's why I didn't mix. Note that my news writer puts my sig at the bottom.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;

And my news writer puts it at the top (OE)!  If I want to bottom-post with sig,
I just cut and paste it to the bottom.  But some newsreaders may not show the
signature explicitly, and instead append it automatically after you send the
message, in which case you are stuck.

MS Outlook and Outlook Express used to default to bottom posting for both e-mail
and news, but sometime around 7-10 years ago IIRC, they switched everything over
to top. At the same time, they also changed the default sort of messages from
newest at the bottom of the list to newest at the top.  So it seemed like an
intentional paradigm shift to always putting the most recent information at the
top of the page.

My \$0.02:  if you are actively following a thread, top posting is easier to deal
with since you always see the latest information immediately.  If you are coming
in late to an existing thread, bottom posting is better since you can read in
natural chronological order.  BTW, the same issue exists with blogs now too!
Most of them are "top-posted" so the latest entry is always the first thing you
see.

--
Jon Harris
SPAM blocked e-mail address in use.  Replace the ANIMAL with 7 to reply.

```