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
sinusoids and aliasing...
Started by ●May 18, 2010
Reply by ●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 ●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 asampling>> frequency f_s at least twice the largest frequency in the signal, canbe>> "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 attwice>> or more its frequency, will give samples that can be the samples ofother>> 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 ●May 19, 20102010-05-19
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
Reply by ●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 ●May 19, 20102010-05-19
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
