Forums

sinusoids and aliasing...

Started by fisico32 May 18, 2010
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

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. �����������������������������������������������������������������������
>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 :)
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 5/19/2010 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 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