1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Confused system stability and linearity

  1. Dec 7, 2011 #1
    confused!!..system stability and linearity

    1)-Is y(n)=cos{x(n)} a stable system??
    and is the condition s=Ʃ|h(k)|<∞ for stability valid only for LTI systems?
    actually my book solves the given problem using the above method..but according to me the given system is not LTI SINCE ZERO I/P does not lead to zero O/P...so i m really confused


    2)to prove system to be linear is it enough to pove that zero i/p leads to zero o/p??
    the system y(t)=[{x(t)}^2] also gives zero o/p on zero i/p but it is not linear...
     
  2. jcsd
  3. Dec 7, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Re: confused!!..system stability and linearity

    No point in subjecting your function cos[x(n)] to a Nyquist test (unit circle stability test) since it's obviously nonlinear.

    You cannot apply the usual expression for the output at discrete multiples of time T. On the other hand, cos[x(nT)] is clearly stable since it can never go beyond +/-1.

    Finally. I must confess with great chagrin that I don't know what the sufficiency test for linearity is with a z transfer function. But clearly you are right in assuming y = cos[x(n)] is nonlinear. I would assume that if the function is a plynomial fraction in z that it is linear. But that is just a not-so-educated guess. :confused:
     
  4. Dec 7, 2011 #3
    Re: confused!!..system stability and linearity

    if the system is linear
    out put for "sum of two different signals" as input should be same as " sum of outputs got when two signals are given separately as input
     
  5. Dec 8, 2011 #4

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Re: confused!!..system stability and linearity

    That's exactly right and is the right answer. So it can be applied equally well to discrete systems, obviously. Thanks reddvoid! Funny how sometimes one doesn't see the woods for the trees!
     
  6. Dec 8, 2011 #5
    Re: confused!!..system stability and linearity

    Actually if the signal satisfy above property the system is "additive". Which is f(x1+x2)=f(x1)+f(x2).

    Additionally the following property, f(λx)=λf(x) is the "homogenity".

    If a system is both "additive" and "homogen" it is said that the system is "linear".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Confused system stability and linearity
  1. Linear system stability (Replies: 10)

Loading...