could anyone help about this equation which is given below y[n]=X^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarient? is it causal? if how.
linear system
Started by ●October 20, 2007
Reply by ●October 20, 20072007-10-20
On Oct 21, 4:12 am, AKBAR <Akbar002...@gmail.com> wrote:> could anyone help about this equation which is given below > > y[n]=X^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarient? > is it causal? if how.i wonder who thinks up these od questions! If you put a sine wave in do you get a sine wave out?(Linear) Does the ouput rely on inputs that are in the future? (uncausal) If you delay the input does the out delay by the same out? (TI?)
Reply by ●October 20, 20072007-10-20
On Sat, 20 Oct 2007 08:36:11 -0700, wabehtdieh wrote:> On Oct 21, 4:12 am, AKBAR <Akbar002...@gmail.com> wrote: >> could anyone help about this equation which is given below >> >> y[n]=X^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarient? >> is it causal? if how. > > i wonder who thinks up these od questions!People assigning homework, mostly.> If you put a sine wave in > do you get a sine wave out?(Linear)Nuh uh. There's a long thread on here that deals with linearity, including the falsity of the above assertion -- you get a sine wave out for a sine wave in if the system is linear, but there are nonlinear systems that pass that test. The definitive test for a linear system is superposition: a system is linear if and only if it obeys superposition. 'nuff said. Here's a Wikipedia entry on the subject: http://en.wikipedia.org/wiki/Linear_system.> Does the ouput rely on inputs that are in the future? (uncausal) > If you delay the input does the out delay by the same out? (TI?)-- Tim Wescott Control systems and communications consulting http://www.wescottdesign.com Need to learn how to apply control theory in your embedded system? "Applied Control Theory for Embedded Systems" by Tim Wescott Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
Reply by ●October 20, 20072007-10-20
"AKBAR" <Akbar002426@gmail.com> wrote in message news:1192893149.355048.245210@e34g2000pro.googlegroups.com...> could anyone help about this equation which is given below > > y[n]=X^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarient? > is it causal? if how. >No, it is not linear because, the squaring factor will produce frequencies that were not originally present, (remember the identities of sin^2), as will X[n-1]X[n+1] It appears to be time-invariant because the time itself does not feature as a factor and only appears as an index It is not causal because X[n+1] is in the future. So, No, Yes, No.
Reply by ●October 20, 20072007-10-20
Anonymous. wrote:> "AKBAR" <Akbar002426@gmail.com> wrote in message > news:1192893149.355048.245210@e34g2000pro.googlegroups.com... >> could anyone help about this equation which is given below >> >> y[n]=X^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarient? >> is it causal? if how. >> > > No, it is not linear because, the squaring factor will produce frequencies > that were > not originally present, (remember the identities of sin^2), as will > X[n-1]X[n+1] > > It appears to be time-invariant because the time itself does not feature as > a factor and only > appears as an index > > It is not causal because X[n+1] is in the future. > > So, No, Yes, No.Shit! you do the OP no favor in the long run by doing his homework. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●October 21, 20072007-10-21
On Oct 21, 5:08 am, Tim Wescott <t...@seemywebsite.com> wrote:> On Sat, 20 Oct 2007 08:36:11 -0700, wabehtdieh wrote: > > On Oct 21, 4:12 am, AKBAR <Akbar002...@gmail.com> wrote: > >> could anyone help about this equation which is given below > > >> y[n]=X^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarient? > >> is it causal? if how. > > > i wonder who thinks up these od questions! > > People assigning homework, mostly. > > > If you put a sine wave in > > do you get a sine wave out?(Linear) > > Nuh uh. There's a long thread on here that deals with linearity, > including the falsity of the above assertion -- you get a sine wave out > for a sine wave in if the system is linear, but there are nonlinear > systems that pass that test.Show me one? Wab
Reply by ●October 21, 20072007-10-21
wabehtdieh@alumni.com wrote:> On Oct 21, 5:08 am, Tim Wescott <t...@seemywebsite.com> wrote: >> On Sat, 20 Oct 2007 08:36:11 -0700, wabehtdieh wrote: >>> On Oct 21, 4:12 am, AKBAR <Akbar002...@gmail.com> wrote: >>>> could anyone help about this equation which is given below >>>> y[n]=X^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarient? >>>> is it causal? if how. >>> i wonder who thinks up these od questions! >> People assigning homework, mostly. >> >>> If you put a sine wave in >>> do you get a sine wave out?(Linear) >> Nuh uh. There's a long thread on here that deals with linearity, >> including the falsity of the above assertion -- you get a sine wave out >> for a sine wave in if the system is linear, but there are nonlinear >> systems that pass that test. > > Show me one? > > WabLinear for small signals, clips for large ones. A small sine wave comes out as such. A very large one comes our nearly square. There are others. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●October 22, 20072007-10-22
On Oct 21, 4:41 am, wabehtd...@alumni.com wrote:> On Oct 21, 5:08 am, Tim Wescott <t...@seemywebsite.com> wrote: > > > > > On Sat, 20 Oct 2007 08:36:11 -0700, wabehtdieh wrote:...> > > If you put a sine wave in > > > do you get a sine wave out?(Linear) > > > Nuh uh. There's a long thread on here that deals with linearity, > > including the falsity of the above assertion -- you get a sine wave out > > for a sine wave in if the system is linear, but there are nonlinear > > systems that pass that test. > > Show me one?how about y(t) = T_n( x(t) * ( 2*LPF(x^2(t)) )^(-1/2) ) where T_n(x) is a Chebyshev polynomial. or did you mean one where the frequency coming out is the same as the frequency going in? r b-j
Reply by ●October 22, 20072007-10-22
On Sun, 21 Oct 2007 01:41:43 -0700, wabehtdieh wrote:> On Oct 21, 5:08 am, Tim Wescott <t...@seemywebsite.com> wrote: >> On Sat, 20 Oct 2007 08:36:11 -0700, wabehtdieh wrote: >> > On Oct 21, 4:12 am, AKBAR <Akbar002...@gmail.com> wrote: >> >> could anyone help about this equation which is given below >> >> >> y[n]=X^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarient? >> >> is it causal? if how. >> >> > i wonder who thinks up these od questions! >> >> People assigning homework, mostly. >> >> > If you put a sine wave in >> > do you get a sine wave out?(Linear) >> >> Nuh uh. There's a long thread on here that deals with linearity, >> including the falsity of the above assertion -- you get a sine wave out >> for a sine wave in if the system is linear, but there are nonlinear >> systems that pass that test. > > Show me one? > > WabConsider a system that examines an input signal for it's frequency content, picks out the lowest-frequency component, and applies that component to the output. This system will, indeed, generate a sine wave (of the correct frequency, even!) when it is presented with a sine wave. It would not, however, follow superposition. This sounds contrived. But then, the whole idea of a "linear system" is contrived as a means to make mathematical analysis of systems easier, so don't quibble. -- Tim Wescott Control systems and communications consulting http://www.wescottdesign.com Need to learn how to apply control theory in your embedded system? "Applied Control Theory for Embedded Systems" by Tim Wescott Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
Reply by ●October 22, 20072007-10-22
On Oct 21, 8:42 am, Jerry Avins <j...@ieee.org> wrote:> Anonymous. wrote: > > "AKBAR" <Akbar002...@gmail.com> wrote in message > >news:1192893149.355048.245210@e34g2000pro.googlegroups.com... > >> could anyone help about this equation which is given below > > >> y[n]=3DX^2[n]-X[n-1]X[n+1] is this system is linear?is it time invarie=nt?> >> is it causal? if how. > > > No, it is not linear because, the squaring factor will produce frequenc=ies> > that were > > not originally present, (remember the identities of sin^2), as will > > X[n-1]X[n+1] > > > It appears to be time-invariant because the time itself does not featur=e as> > a factor and only > > appears as an index > > > It is not causal because X[n+1] is in the future. > > > So, No, Yes, No. > > Shit! you do the OP no favor in the long run by doing his homework. > > 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 hmm...that applies to nearly all real-world systems - they all saturate eventually. I would still call that linear just as I would call an op-amp with feedback linear. Would you really say an op-amp was non-linear just because it saturates? Hardy
