> 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
Reply by Jerry Avins●May 19, 20102010-05-19
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.
�����������������������������������������������������������������������
Reply by glen herrmannsfeldt●May 19, 20102010-05-19
> 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
Reply by fisico32●May 18, 20102010-05-18
>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.
>�����������������������������������������������������������������������
>you are right, what am I talking about, i am too tired :)
Reply by Jerry Avins●May 18, 20102010-05-18
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.
�����������������������������������������������������������������������
Reply by fisico32●May 18, 20102010-05-18
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