# Sampling Problems

Started by July 1, 2005
```I'm writing some material about sampling for the beginner.  I want to
include a bit about non-ideal sampling.  Assuming that sampling is
defined as a process that takes on the value of a continuous-time signal
at the instant that t = (sample time) * n, the only difficulties that I
can attribute to the sampling process itself are:

1.  Finite Aperture, i.e. the signal will be filtered a little bit
before sampling.

2.  Jitter, i.e. the actual sample time will vary from the assumed
sample time by some amount.

What have I missed?

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

```
```Tim Wescott wrote:
> I'm writing some material about sampling for the beginner.  I want to
> include a bit about non-ideal sampling.  Assuming that sampling is
> defined as a process that takes on the value of a continuous-time signal
> at the instant that t = (sample time) * n, the only difficulties that I
> can attribute to the sampling process itself are:
>
> 1.  Finite Aperture, i.e. the signal will be filtered a little bit
> before sampling.
>
> 2.  Jitter, i.e. the actual sample time will vary from the assumed
> sample time by some amount.
>
> What have I missed?

From a practical point of view? Capacitor memory (dielectric
absorption) and S&H leakage mess up the samples too. I'm sure there's more.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```Jerry Avins wrote:

> Tim Wescott wrote:
>
>> I'm writing some material about sampling for the beginner.  I want to
>> include a bit about non-ideal sampling.  Assuming that sampling is
>> defined as a process that takes on the value of a continuous-time
>> signal at the instant that t = (sample time) * n, the only
>> difficulties that I can attribute to the sampling process itself are:
>>
>> 1.  Finite Aperture, i.e. the signal will be filtered a little bit
>> before sampling.
>>
>> 2.  Jitter, i.e. the actual sample time will vary from the assumed
>> sample time by some amount.
>>
>> What have I missed?
>
>
>  From a practical point of view? Capacitor memory (dielectric
> absorption) and S&H leakage mess up the samples too. I'm sure there's more.
>
Hadn't thought of those -- but if you sample fast enough leakage isn't
much of an issue.  Modern C-2C ADCs do have a problem which is that when
the sampling switch is closed some of the charge can leak back into an
insufficiently stiff driver so the new reading depends ever so slightly
on the old.

--
-------------------------------------------
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
```
```Tim Wescott wrote:
> Jerry Avins wrote:
>
>> Tim Wescott wrote:
>>
>>> I'm writing some material about sampling for the beginner.  I want to
>>> include a bit about non-ideal sampling.  Assuming that sampling is
>>> defined as a process that takes on the value of a continuous-time
>>> signal at the instant that t = (sample time) * n, the only
>>> difficulties that I can attribute to the sampling process itself are:
>>>
>>> 1.  Finite Aperture, i.e. the signal will be filtered a little bit
>>> before sampling.
>>>
>>> 2.  Jitter, i.e. the actual sample time will vary from the assumed
>>> sample time by some amount.
>>>
>>> What have I missed?
>>
>>
>>
>>  From a practical point of view? Capacitor memory (dielectric
>> absorption) and S&H leakage mess up the samples too. I'm sure there's
>> more.
>>
> Hadn't thought of those -- but if you sample fast enough leakage isn't
> much of an issue.  Modern C-2C ADCs do have a problem which is that when
> the sampling switch is closed some of the charge can leak back into an
> insufficiently stiff driver so the new reading depends ever so slightly
> on the old.

The faster you want to sample, the smaller the capacitor you can afford,
so leakage is pretty constant when scaled by sample time.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```Might want to discuss anti-aliasing filtering topics including,
avoiding aliasing, phase effects, and possibility of compromises
between filtering, signal bandwidth, and sample rate.

Might want to look at/discuss sigma-delta/delta-sigma converters.

Dirk

Tim Wescott wrote:
> I'm writing some material about sampling for the beginner.  I want to
> include a bit about non-ideal sampling.  Assuming that sampling is
> defined as a process that takes on the value of a continuous-time signal
> at the instant that t = (sample time) * n, the only difficulties that I
> can attribute to the sampling process itself are:
>
> 1.  Finite Aperture, i.e. the signal will be filtered a little bit
> before sampling.
>
> 2.  Jitter, i.e. the actual sample time will vary from the assumed
> sample time by some amount.
>
> What have I missed?
>
> -------------------------------------------
> Tim Wescott
> Wescott Design Services
> http://www.wescottdesign.com

```
```dbell wrote:

(top posting compulsively "corrected")

> Tim Wescott wrote:
>
>>I'm writing some material about sampling for the beginner.  I want to
>>include a bit about non-ideal sampling.  Assuming that sampling is
>>defined as a process that takes on the value of a continuous-time signal
>>at the instant that t = (sample time) * n, the only difficulties that I
>>can attribute to the sampling process itself are:
>>
>>1.  Finite Aperture, i.e. the signal will be filtered a little bit
>>before sampling.
>>
>>2.  Jitter, i.e. the actual sample time will vary from the assumed
>>sample time by some amount.
>>
>>What have I missed?
>>
>>-------------------------------------------
>>Tim Wescott
>>Wescott Design Services
>>http://www.wescottdesign.com
>
>
> Might want to discuss anti-aliasing filtering topics including,
> avoiding aliasing, phase effects, and possibility of compromises
> between filtering, signal bandwidth, and sample rate.
>
> Might want to look at/discuss sigma-delta/delta-sigma converters.
>
Yes, I'm introducing the concepts of aliasing, discussing anti-alias
filters and their drawbacks, why you want your anti-alias filter to be
of lower order and wider in a control context than you would in a pure
signal processing context, etc.

I hadn't considered discussing converters at all -- perhaps if there's
room I will discuss converters in general, however.

-------------------------------------------
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
```
```I did a detector noise limited design for IR detection back in the
80's.  You could practically write a whole book on the sample and hold
section.  Nothing is "perfect".  You have to choose an imperfect
material for the capcitor and imperfect switches, and then work around
the imperfections, deal with the response time of the circuit, the
spectral content of the noise and signal.  The problems and solutions
just go on and on; totally satisfying as a design project :)
In the end though we had a 100ppm precision, offset/leakage
compensation, 1kHz sampling rate, 5 channels, and detector noise
limited  system.
The first (and last) thing is learning how to do fast estimates, then
you can proceed towards detailed calculations.  All of the first order
errors can be cancelled then you are left with the second order errors
that typically must be esamined in detail, including interactions; then
you have a stable good system you have control of.  Believe it or not
the second order errors hold surprises.  It sounds hard but it is all
standard Electronic theory applied in detail.
The final sampling circuit only had about 4-5 parts; it's all in timing
and process.

Ray

```
```RRogers wrote:
> I did a detector noise limited design for IR detection back in the
> 80's.  You could practically write a whole book on the sample and hold
> section.  Nothing is "perfect".  You have to choose an imperfect
> material for the capcitor and imperfect switches, and then work around
> the imperfections, deal with the response time of the circuit, the
> spectral content of the noise and signal.  The problems and solutions
> just go on and on;

...

>   It sounds hard but it is all
> standard Electronic theory applied in detail.
> The final sampling circuit only had about 4-5 parts; it's all in timing
> and process.

It seems like a difficult job elegantly done. I don't know which is
harder: cataloging (and maybe learning) the elements of good design, or
deciding which of them to include in a beginning course.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```On Fri, 01 Jul 2005 12:46:27 -0700, Tim Wescott <tim@seemywebsite.com>
wrote:
>I'm writing some material about sampling for the beginner.  I want to
>include a bit about non-ideal sampling.  Assuming that sampling is
>defined as a process that takes on the value of a continuous-time signal
>at the instant that t = (sample time) * n, the only difficulties that I
>can attribute to the sampling process itself are:
>1.  Finite Aperture, i.e. the signal will be filtered a little bit
>before sampling.
>2.  Jitter, i.e. the actual sample time will vary from the assumed
>sample time by some amount.
>What have I missed
>Tim Wescott >Wescott Design Services >http://www.wescottdesign.com

How about quantization by the resolution of the converter and the
process of reconstruction of the original signal.  I suppose the
differences in zero and first order hold is inappropriate for the
beginner.

```
```AntiSPAM_g9u5dd43@yahoo.com wrote:
> On Fri, 01 Jul 2005 12:46:27 -0700, Tim Wescott <tim@seemywebsite.com>
> wrote:
>
>>I'm writing some material about sampling for the beginner.  I want to
>>include a bit about non-ideal sampling.  Assuming that sampling is
>>defined as a process that takes on the value of a continuous-time signal
>>at the instant that t = (sample time) * n, the only difficulties that I
>>can attribute to the sampling process itself are:
>>1.  Finite Aperture, i.e. the signal will be filtered a little bit
>>before sampling.
>>2.  Jitter, i.e. the actual sample time will vary from the assumed
>>sample time by some amount.
>>What have I missed
>>Tim Wescott >Wescott Design Services >http://www.wescottdesign.com
>
>
> How about quantization by the resolution of the converter and the
> process of reconstruction of the original signal.  I suppose the
> differences in zero and first order hold is inappropriate for the
> beginner.

As I understand it, no hold at all is a series of spikes, a zero-order
hold creates a stair case, and a first-order hold is either a
continuation of the previous section's slope, of linear interpolation.
The only first-order hold I've ever seen was one I built myself to
smooth the digitally generated carrier of a home-brew 212 modem.

<quibble> A zero-order hold doesn't attenuate the high frequencies. It
greatly amplifies the whole usable spectrum, just a little less at the
high end. </quibble>

Leave out the detail. It's not too deep, but it sidetracks the thought
process. Describe the stepwise nature of the output, mention in passing
(if you must) the high-end loss, but pass on. High-end attenuation is
zilch anyway in servos with their necessary oversampling. MHO.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```