# Doubts in Sampling

Started by September 30, 2009
```Hi,

I have a doubt in Sampling of Signals from a Theoretical Point of View.
When we sample a signal, are we losing anything in terms of Energy of the
signal? Intuitively, it seems so. But I also know that there is no loss of
Information (since the spectrum is still intact, if we sample at a proper
rate). Is my reasoning correct or is it flawed somewhere?

```
```On 1 Okt, 00:27, "macsdev" <macs...@gmail.com> wrote:
> Hi,
>
> I have a doubt in Sampling of Signals from a Theoretical Point of View.
> When we sample a signal, are we losing anything in terms of Energy of the
> signal? Intuitively, it seems so. But I also know that there is no loss of
> Information (since the spectrum is still intact, if we sample at a proper
> rate). Is my reasoning correct or is it flawed somewhere?

Flamebait? OK, here we go:

Once the signal has been sampled, you only have a sequence of
numbers, not a physical quantity. Since no physical quantities
are involved, the term 'energy' has no relevance.

Rune
```
```macsdev wrote:
> Hi,
>
> I have a doubt in Sampling of Signals from a Theoretical Point of View.
> When we sample a signal, are we losing anything in terms of Energy of the
> signal? Intuitively, it seems so. But I also know that there is no loss of
> Information (since the spectrum is still intact, if we sample at a proper
> rate). Is my reasoning correct or is it flawed somewhere?

I suppose there's a way to sample energy, but I don't see what use it
would be. Usually we sample voltage (rarely, current) and those
quantities are signed. What would negative energy signify? What
reasoning do you question?

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;
```
```Ok. I should not have said Theoretical. Say, we have a sinusoidal signal of
frequency f. That Signal has an Energy. When we sample that signal are we
losing anything?

>macsdev wrote:
>> Hi,
>>
>> I have a doubt in Sampling of Signals from a Theoretical Point of
View.
>> When we sample a signal, are we losing anything in terms of Energy of
the
>> signal? Intuitively, it seems so. But I also know that there is no loss
of
>> Information (since the spectrum is still intact, if we sample at a
proper
>> rate). Is my reasoning correct or is it flawed somewhere?
>
>I suppose there's a way to sample energy, but I don't see what use it
>would be. Usually we sample voltage (rarely, current) and those
>quantities are signed. What would negative energy signify? What
>reasoning do you question?
>
>Jerry
>--
>Engineering is the art of making what you want from things you can get.
>&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;
>
```
```>Hi,
>
>I have a doubt in Sampling of Signals from a Theoretical Point of View.
>When we sample a signal, are we losing anything in terms of Energy of
the
>signal? Intuitively, it seems so. But I also know that there is no loss
of
>Information (since the spectrum is still intact, if we sample at a
proper
>rate). Is my reasoning correct or is it flawed somewhere?

How do you define energy?  Based on alternative definitions:

1) Every time your sample/hold circuit dumps the cap, you're throwing away
energy...

2) Even if you can define energy such that it stays the same once you
sample it ideally (some sort of RMS signal strength integrated), your
"energy" likely changes slightly due to quantization.  It may be a net loss
or gain, I think.

3) If you hadn't stipulated no aliasing, and you used E=hf, aliasing
throws away energy.  Not that this definition makes any sense, but I
couldn't resist. :)

```
```macsdev wrote:
> Ok. I should not have said Theoretical. Say, we have a sinusoidal signal of
> frequency f. That Signal has an Energy. When we sample that signal are we
> losing anything?

A sample is a measurement, usually of voltage, always expressed as a
number. What energy do you contemplate in this question?

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;
```
```Rune Allnor <allnor@tele.ntnu.no> wrote in

> On 1 Okt, 00:27, "macsdev" <macs...@gmail.com> wrote:
>> Hi,
>>
>> I have a doubt in Sampling of Signals from a Theoretical Point of
>> View. When we sample a signal, are we losing anything in terms of
>> Energy of the signal? Intuitively, it seems so. But I also know that
>> there is no loss of Information (since the spectrum is still intact,
>> if we sample at a proper rate). Is my reasoning correct or is it
>> flawed somewhere?
>
> Flamebait? OK, here we go:
>
> Once the signal has been sampled, you only have a sequence of
> numbers, not a physical quantity. Since no physical quantities
> are involved, the term 'energy' has no relevance.
>
> Rune

I doubt that the OP really means what he says, but that's a separate issue.
The fact of the matter is that unless you want to redefine the classical
other than pure unadulterated bull shit.  By definition, if you have an
energy density spectrum and integrate it, you get total signal energy.
```
```On 9/30/2009 6:00 PM, Jimmy J wrote:
> Rune Allnor<allnor@tele.ntnu.no>  wrote in
>
>> On 1 Okt, 00:27, "macsdev"<macs...@gmail.com>  wrote:
>>> Hi,
>>>
>>> I have a doubt in Sampling of Signals from a Theoretical Point of
>>> View. When we sample a signal, are we losing anything in terms of
>>> Energy of the signal? Intuitively, it seems so. But I also know that
>>> there is no loss of Information (since the spectrum is still intact,
>>> if we sample at a proper rate). Is my reasoning correct or is it
>>> flawed somewhere?
>> Flamebait? OK, here we go:
>>
>> Once the signal has been sampled, you only have a sequence of
>> numbers, not a physical quantity. Since no physical quantities
>> are involved, the term 'energy' has no relevance.
>>
>> Rune
>
>
> I doubt that the OP really means what he says, but that's a separate issue.
> The fact of the matter is that unless you want to redefine the classical
> concept and definition of energy spectral density, your reply is nothing
> other than pure unadulterated bull shit.  By definition, if you have an
> energy density spectrum and integrate it, you get total signal energy.

He didn't say he had an energy density spectrum (whatever that is), so I
wouldn't assume he can integrate anything to get energy.

More to the point, concepts like power and energy are only meaningful to
discrete sequences for which those values may be relevant.  A sequence
of numbers representing total daily rainfall over a number of days is
unlikely to provide information in terms of Joules or Watts.  A sequence
of numbers representing a voltage measured over known time periods on a
fixed impedance may, however.

I think what Rune was saying was that the sequence of numbers has no
energy itself, which is true, and I'm pointing out that IF the units of
the measured samples lend themselves to computing energy for the signal
sampled then that can certainly be done.

One always has to be careful to properly interpret the results of any
process.  Computing the "Power Spectral Density" of the sequence
representing the gas volume of successive tokes on the bong won't yield
Watts/Hz.

--
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com
```
```Eric Jacobsen <eric.jacobsen@ieee.org> wrote in

> On 9/30/2009 6:00 PM, Jimmy J wrote:
>> Rune Allnor<allnor@tele.ntnu.no>  wrote in
>>
>>> On 1 Okt, 00:27, "macsdev"<macs...@gmail.com>  wrote:
>>>> Hi,
>>>>
>>>> I have a doubt in Sampling of Signals from a Theoretical Point of
>>>> View. When we sample a signal, are we losing anything in terms of
>>>> Energy of the signal? Intuitively, it seems so. But I also know
>>>> that there is no loss of Information (since the spectrum is still
>>>> intact, if we sample at a proper rate). Is my reasoning correct or
>>>> is it flawed somewhere?
>>> Flamebait? OK, here we go:
>>>
>>> Once the signal has been sampled, you only have a sequence of
>>> numbers, not a physical quantity. Since no physical quantities
>>> are involved, the term 'energy' has no relevance.
>>>
>>> Rune
>>
>>
>> I doubt that the OP really means what he says, but that's a separate
>> issue. The fact of the matter is that unless you want to redefine the
>> classical concept and definition of energy spectral density, your
>> definition, if you have an energy density spectrum and integrate it,
>> you get total signal energy.
>
> He didn't say he had an energy density spectrum (whatever that is), so
> I wouldn't assume he can integrate anything to get energy.
>
> More to the point, concepts like power and energy are only meaningful
> to discrete sequences for which those values may be relevant.  A
> sequence of numbers representing total daily rainfall over a number of
> days is unlikely to provide information in terms of Joules or Watts.
> A sequence of numbers representing a voltage measured over known time
> periods on a fixed impedance may, however.
>
> I think what Rune was saying was that the sequence of numbers has no
> energy itself, which is true, and I'm pointing out that IF the units
> of the measured samples lend themselves to computing energy for the
> signal sampled then that can certainly be done.
>
> One always has to be careful to properly interpret the results of any
> process.  Computing the "Power Spectral Density" of the sequence
> representing the gas volume of successive tokes on the bong won't
> yield Watts/Hz.

For whatever reason, you seem to have either missed or intentionally
ignored the first half dozen or so words of the OP which were "I have a
doubt in Sampling of Signals."  Energy spectral density and power
spectral density are defined specifically with reference to the analysis
of "signals."  The issue of whether or not the OP has available an energy
density spectrum is irrelevant.  My comment pertained to Rune Allnor's
idiotic and false statement "Since no physical quantities are involved,
the term 'energy' has no relevance."  Whether you and Rhune Allnor are
willing to admit it or not, signal energy is a physical quantity, by
definition.

```
```Jimmy J wrote:
> Eric Jacobsen <eric.jacobsen@ieee.org> wrote in
>
>> On 9/30/2009 6:00 PM, Jimmy J wrote:
>>> Rune Allnor<allnor@tele.ntnu.no>  wrote in
>>>
>>>> On 1 Okt, 00:27, "macsdev"<macs...@gmail.com>  wrote:
>>>>> Hi,
>>>>>
>>>>> I have a doubt in Sampling of Signals from a Theoretical Point of
>>>>> View. When we sample a signal, are we losing anything in terms of
>>>>> Energy of the signal? Intuitively, it seems so. But I also know
>>>>> that there is no loss of Information (since the spectrum is still
>>>>> intact, if we sample at a proper rate). Is my reasoning correct or
>>>>> is it flawed somewhere?
>>>> Flamebait? OK, here we go:
>>>>
>>>> Once the signal has been sampled, you only have a sequence of
>>>> numbers, not a physical quantity. Since no physical quantities
>>>> are involved, the term 'energy' has no relevance.
>>>>
>>>> Rune
>>>
>>> I doubt that the OP really means what he says, but that's a separate
>>> issue. The fact of the matter is that unless you want to redefine the
>>> classical concept and definition of energy spectral density, your
>>> definition, if you have an energy density spectrum and integrate it,
>>> you get total signal energy.
>> He didn't say he had an energy density spectrum (whatever that is), so
>> I wouldn't assume he can integrate anything to get energy.
>>
>> More to the point, concepts like power and energy are only meaningful
>> to discrete sequences for which those values may be relevant.  A
>> sequence of numbers representing total daily rainfall over a number of
>> days is unlikely to provide information in terms of Joules or Watts.
>> A sequence of numbers representing a voltage measured over known time
>> periods on a fixed impedance may, however.
>>
>> I think what Rune was saying was that the sequence of numbers has no
>> energy itself, which is true, and I'm pointing out that IF the units
>> of the measured samples lend themselves to computing energy for the
>> signal sampled then that can certainly be done.
>>
>> One always has to be careful to properly interpret the results of any
>> process.  Computing the "Power Spectral Density" of the sequence
>> representing the gas volume of successive tokes on the bong won't
>> yield Watts/Hz.
>
>
> For whatever reason, you seem to have either missed or intentionally
> ignored the first half dozen or so words of the OP which were "I have a
> doubt in Sampling of Signals."  Energy spectral density and power
> spectral density are defined specifically with reference to the analysis
> of "signals."  The issue of whether or not the OP has available an energy
> density spectrum is irrelevant.  My comment pertained to Rune Allnor's
> idiotic and false statement "Since no physical quantities are involved,
> the term 'energy' has no relevance."  Whether you and Rhune Allnor are
> willing to admit it or not, signal energy is a physical quantity, by
> definition.

You have asserted in the past that you know little or nothing about DSP.
Here, you removed all doubt.

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;
```