```fisico32 wrote:
> Hello forum,
>
> while a composite signal (made of many sinusoids), if sampled at a sampling
> frequency f_s at least twice the largest frequency in the signal, can  be
> "uniquely" reconstructed from its samples,
> a continuous pure sinusoid of freq f instead, no matter if sampled at twice
> or more its frequency, will give samples that can be the samples of other
> sinuosids, all those with frequency f+-n*f_s where f_s the sampling
> frequency....
>
> The sampling criterion then works only for a signal with more than one
> sinusoid...
>
> Am I correct?

No.  Think.

What is the process that they use to reconstruct that complex signal
from the sampled one?  What happens when you attempt to reconstruct a
sampled single sinusoidal signal, using that process?  (what happens
when you try to say "sampled single sinusoidal signal" three times fast?).

Finally: Is the sampling and reconstruction process a linear process?
If you think it isn't, explain.  If you think it is, how can you
reconstruct a complex signal but not a simple one?

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
```
```On 5/19/2010 12:14 AM, glen herrmannsfeldt wrote:

...

> Well, a single sinusoid could be the sum of many, with most
> having an amplitude of zero...

There's a minor problem there. I'll discuss it in public once Fisico
works out for himself where he went wrong.

Jerry
--
"I view the progress of science as ... the slow erosion of the tendency
to dichotomize." --Barbara Smuts, U. Mich.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```fisico32 <marcoscipioni1@n_o_s_p_a_m.gmail.com> wrote:

> while a composite signal (made of many sinusoids), if sampled at
> a sampling frequency f_s at least twice the largest frequency in
> the signal, can  be "uniquely" reconstructed from its samples,

Technically only for an infinite number of samples, or for
a periodic signal.  Close enough in most cases.

> a continuous pure sinusoid of freq f instead, no matter if
> sampled at twice or more its frequency, will give samples
> that can be the samples of other sinuosids, all those with
> frequency f+-n*f_s where f_s the sampling frequency....

A single sinusoid of unknown amplitude, phase, and frequency
can usually be reconstructed from a small number of samples,
such as three or four, unless you are very unlucky.

> The sampling criterion then works only for a signal with more
> than one sinusoid...

Well, a single sinusoid could be the sum of many, with most
having an amplitude of zero...

-- glen
```
```>On 5/18/2010 10:07 PM, fisico32 wrote:
>> Hello forum,
>>
>> while a composite signal (made of many sinusoids), if sampled at a
sampling
>> frequency f_s at least twice the largest frequency in the signal, can
be
>> "uniquely" reconstructed from its samples,
>
>Not really. You left out an important criterion.
>
>> a continuous pure sinusoid of freq f instead, no matter if sampled at
twice
>> or more its frequency, will give samples that can be the samples of
other
>> sinuosids, all those with frequency f+-n*f_s where f_s the sampling
>> frequency....
>>
>> The sampling criterion then works only for a signal with more than one
>> sinusoid...
>>
>> Am I correct?
>
>No.
>
>Jerry
>--
>"I view the progress of science as ... the slow erosion of the tendency
>  to dichotomize." --Barbara Smuts, U. Mich.
>&#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;
>you are right, what am I talking about, i am too tired :)
```
```On 5/18/2010 10:07 PM, fisico32 wrote:
> Hello forum,
>
> while a composite signal (made of many sinusoids), if sampled at a sampling
> frequency f_s at least twice the largest frequency in the signal, can  be
> "uniquely" reconstructed from its samples,

Not really. You left out an important criterion.

> a continuous pure sinusoid of freq f instead, no matter if sampled at twice
> or more its frequency, will give samples that can be the samples of other
> sinuosids, all those with frequency f+-n*f_s where f_s the sampling
> frequency....
>
> The sampling criterion then works only for a signal with more than one
> sinusoid...
>
> Am I correct?

No.

Jerry
--
"I view the progress of science as ... the slow erosion of the tendency
to dichotomize." --Barbara Smuts, U. Mich.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```Hello forum,

while a composite signal (made of many sinusoids), if sampled at a sampling
frequency f_s at least twice the largest frequency in the signal, can  be
"uniquely" reconstructed from its samples,
a continuous pure sinusoid of freq f instead, no matter if sampled at twice
or more its frequency, will give samples that can be the samples of other
sinuosids, all those with frequency f+-n*f_s where f_s the sampling
frequency....

The sampling criterion then works only for a signal with more than one
sinusoid...

Am I correct?
thanks
fisico32

```