1. Not finding help here? Sign up for a free 30min 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!

Determining if a System is Time-Invariant and/or Linear

  1. May 6, 2012 #1
    1. The problem statement, all variables and given/known data
    For each of the following systems, determine whether or not the system is Time-Invariant, Linear, and causal.

    a.) y[n] = x[n]cos(0.2*pi*n)
    there are more but if I can figure this out I should be able to get the others


    2. Relevant equations
    Time Invariant ---> if x[n] produces y[n] then x[n - d] produces y[n - d]
    Linear ---> if x1[n] produces y1[n] and x2[n] produces y2[n], then x[n] = ax1[n] + bx2[n] produces y[n]=ay1[n] + by2[n]


    3. The attempt at a solution
    I am able to prove that y[n] = x[n]cos(0.2*pi*n) is linear by saying
    let x[n] = ax1[n] + bx2[n]
    then y[n] = (ax1[n] + bx2[n])cos(0.2*pi*n) = ax1[n]cos(0.2*pi*n) + bx2[n]cos(0.2*pi*n)
    so y[n] = ay1[n] + by2[n] proving that it is linear

    I am not able to prove, at this point, that y[n] is either time-invariant or not.
    All I have is this:
    let g[n] = x[n - d]
    then y[n - d] = g[n]cos(0.2*pi*n) = x[n - d]cos(0.2*pi*n), so it is time-invariant?
    This doesn't seem right though for whatever reason.
     
  2. jcsd
  3. May 8, 2012 #2

    Päällikkö

    User Avatar
    Homework Helper

    The system is time invariant if it gives the same output regardless of whether a delay is made to the input signal, or to the output signal.
    So, given
    y[n] = x[n]cos(0.2*pi*n)
    If the output signal is delayed,
    y[n-d] = x[n-d]cos(0.2*pi*(n-d))
    However, if the delay was made to the input signal, before inputing it into the system ... Can you take it from here?
     
  4. May 8, 2012 #3
    Im following you until you talk about making the delay prior to inputting the signal.

    Let me see if I am understanding. It looks to me like, unless you pick a d that delays it by 2*pi*k where k is an interger, it wont produce the same output?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Determining if a System is Time-Invariant and/or Linear
Loading...