dear all, I know the definition of a causal system in the textbook: the output depends only on past and current inputs and doesn't depend on future inputs. Today my prof tells us: a system is causal<=> the output becomes nonzero after the input becomes non-zero. Would any one tell me what is the definition. I cannot find the relation between two definitions. Thanks
causal system, ??? plz hlp
Started by ●August 15, 2005
Reply by ●August 15, 20052005-08-15
On 15 Aug 2005 08:21:10 -0700, VijaKhara@gmail.com wrote:>dear all, > >I know the definition of a causal system in the textbook: the output >depends only on past and current inputs and doesn't depend on future >inputs. >Today my prof tells us: a system is causal<=> the output becomes >nonzero after the input becomes non-zero. >Would any one tell me what is the definition. I cannot find the >relation between two definitions. > >Thanksso y(t) = 5 + x(t) is not casual ?
Reply by ●August 15, 20052005-08-15
VijaKhara@gmail.com wrote:> dear all, > > I know the definition of a causal system in the textbook: the output > depends only on past and current inputs and doesn't depend on future > inputs. > Today my prof tells us: a system is causal <=> the output becomes > nonzero after the input becomes non-zero.All realizable circuits and devices are causal,claims of prognosticators notwithstanding; otherwise predicting the future would be commonplace. It is easy to display a causal oscillator that violates your prof's condition, so I don't believe it. Did you hear him right?> Would any one tell me what is the definition. I cannot find the > relation between two definitions.Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 15, 20052005-08-15
VijaKhara@gmail.com skrev:> dear all, > > I know the definition of a causal system in the textbook: the output > depends only on past and current inputs and doesn't depend on future > inputs. > Today my prof tells us: a system is causal<=> the output becomes > nonzero after the input becomes non-zero.I almost agree with him. If the input signal x[n] == 0 for n<0, then the output y[n]== 0 for n<0. If x[0] =/= 0, then y[0] may or may not be 0. What you write above goes a step too far in unconditionally claiming that y[0]== 0.> Would any one tell me what is the definition. I cannot find the > relation between two definitions.Basically, a causal system ccan not react (i.e. become non-zero) before some non-zero sample has appeared on the input. Does that help? Rune
Reply by ●August 15, 20052005-08-15
VijaKhara@gmail.com wrote:> dear all, > > I know the definition of a causal system in the textbook: the output > depends only on past and current inputs and doesn't depend on future > inputs. > Today my prof tells us: a system is causal<=> the output becomes > nonzero after the input becomes non-zero. > Would any one tell me what is the definition. I cannot find the > relation between two definitions. > > Thanks >Your professor's definition only holds for a linear system (see Jerry's and "mk"'s answers for counterexamples using non-linear systems). If you say "A linear system is causal if and only if the output becomes non zero after the input becomes non zero." it should make more sense. <RANT> Why do schools get so bound up in teaching linear systems when such things _do not_ exist in the real word? Teaching linear systems as a good approximation to the real world is a _good_ thing, because there's so much math that you can do so much easier if you assume linear systems. Forgetting that _real_ systems are _always_ non-linear is a _bad thing_ because then you forget how to do real things with all your knowledge. And don't get me started on the stationary Gaussian process assumption... </RANT> -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●August 15, 20052005-08-15
Tim Wescott skrev:> VijaKhara@gmail.com wrote: > > > dear all, > > > > I know the definition of a causal system in the textbook: the output > > depends only on past and current inputs and doesn't depend on future > > inputs. > > Today my prof tells us: a system is causal<=> the output becomes > > nonzero after the input becomes non-zero. > > Would any one tell me what is the definition. I cannot find the > > relation between two definitions. > > > > Thanks > > > Your professor's definition only holds for a linear system (see Jerry's > and "mk"'s answers for counterexamples using non-linear systems). If > you say "A linear system is causal if and only if the output becomes non > zero after the input becomes non zero." it should make more sense. > > <RANT> > > Why do schools get so bound up in teaching linear systems when such > things _do not_ exist in the real word? Teaching linear systems as a > good approximation to the real world is a _good_ thing, because there's > so much math that you can do so much easier if you assume linear > systems. Forgetting that _real_ systems are _always_ non-linear is a > _bad thing_ because then you forget how to do real things with all your > knowledge. > > And don't get me started on the stationary Gaussian process assumption...These things are taught because they are what appear in the textbooks. No professor or TA I know of, have sufficient practical experience to comment on these things in class, let alone write a textbook that actually discusses such "minor" deviations from "standard" theory. It's basically a deadlock: No one learn the difference, and those who ought to teach don't, since they would need to learn the importance of the difference first. Which they don't since they already know what there is to know about the field. They are professors, right?> </RANT>/Rune
Reply by ●August 15, 20052005-08-15
Hi all, thank u very much. I have checked the note, his statement is only for a linear system. Sorry. Jerry Avins wrote:> VijaKhara@gmail.com wrote: > > dear all, > > > > I know the definition of a causal system in the textbook: the output > > depends only on past and current inputs and doesn't depend on future > > inputs. > > Today my prof tells us: a system is causal <=3D> the output becomes > > nonzero after the input becomes non-zero. > > All realizable circuits and devices are causal,claims of prognosticators > notwithstanding; otherwise predicting the future would be commonplace. > It is easy to display a causal oscillator that violates your prof's > condition, so I don't believe it. Did you hear him right? > > > Would any one tell me what is the definition. I cannot find the > > relation between two definitions. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF==AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF
Reply by ●August 15, 20052005-08-15
VijaKhara@gmail.com wrote:> Hi all, thank u very much. I have checked the note, his statement is > only for a linear system. Sorry.Mk's construct, 5 + f(t), is a linear counterexample> Jerry Avins wrote: > >>VijaKhara@gmail.com wrote: >> >>>dear all, >>> >>>I know the definition of a causal system in the textbook: the output >>>depends only on past and current inputs and doesn't depend on future >>>inputs. >>>Today my prof tells us: a system is causal <=> the output becomes >>>nonzero after the input becomes non-zero. >> >>All realizable circuits and devices are causal,claims of prognosticators >>notwithstanding; otherwise predicting the future would be commonplace. >>It is easy to display a causal oscillator that violates your prof's >>condition, so I don't believe it. Did you hear him right? >> >> >>>Would any one tell me what is the definition. I cannot find the >>>relation between two definitions. >> >>Jerry >>-- >>Engineering is the art of making what you want from things you can get. >>����������������������������������������������������������������������� > >-- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 15, 20052005-08-15
Rune Allnor wrote:> VijaKhara@gmail.com skrev: > >>dear all, >> >>I know the definition of a causal system in the textbook: the output >>depends only on past and current inputs and doesn't depend on future >>inputs. >>Today my prof tells us: a system is causal<=> the output becomes >>nonzero after the input becomes non-zero. > > > I almost agree with him. If the input signal x[n] == 0 for n<0, > then the output y[n]== 0 for n<0. If x[0] =/= 0, then y[0] may > or may not be 0. What you write above goes a step too far in > unconditionally claiming that y[0]== 0. > > >>Would any one tell me what is the definition. I cannot find the >>relation between two definitions. > > > Basically, a causal system ccan not react (i.e. become non-zero) > before some non-zero sample has appeared on the input. > > Does that help?It doesn't help me. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 15, 20052005-08-15
Tim Wescott wrote:> VijaKhara@gmail.com wrote: > >> dear all, >> >> I know the definition of a causal system in the textbook: the output >> depends only on past and current inputs and doesn't depend on future >> inputs. >> Today my prof tells us: a system is causal<=> the output becomes >> nonzero after the input becomes non-zero. >> Would any one tell me what is the definition. I cannot find the >> relation between two definitions. >> >> Thanks >> > Your professor's definition only holds for a linear system (see Jerry's > and "mk"'s answers for counterexamples using non-linear systems). If > you say "A linear system is causal if and only if the output becomes non > zero after the input becomes non zero." it should make more sense. > > <RANT> > > Why do schools get so bound up in teaching linear systems when such > things _do not_ exist in the real word? Teaching linear systems as a > good approximation to the real world is a _good_ thing, because there's > so much math that you can do so much easier if you assume linear > systems. Forgetting that _real_ systems are _always_ non-linear is a > _bad thing_ because then you forget how to do real things with all your > knowledge. > > And don't get me started on the stationary Gaussian process assumption... > > </RANT>I guess I need to hit the books again. How is y[t] = A + x[t] not linear? I understand "A linear system is causal if and only if 1) the output is equal to some constant for all t < T_0, during which time the input is zero. 2) the output becomes returns to that constant a finite time after the input becomes zero." Why bother? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
