signal help

Discussion in 'Homework Help' started by Xufyan, Aug 2, 2011.

  1. Xufyan

    Thread Starter Member

    Aug 3, 2010
    114
    0
    1. The problem statement, all variables and given/known data

    Solvinf the unit time step equation mathematically.
    2. Relevant equations

    x(t) = u(t+1) - 2u(t) + u(t-1)
    3. The attempt at a solution
    How can i solve this signal mathemtically :( and using plotted signals , i couldn't understand,
    here is my approach and i'm not sure it is correct,
    i simply wrote the coordiantes of each signal,
    u(t+1) = (-1,1)
    -2ut = (0,-2)
    u(t-1) = (1,1)
    and then added them which give answer = '0' :(
    is this the way of solving the signals ?
    please help
     
  2. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Give values to t, 0 1 2 3 and so on.

    At each value evaluate each term in the equation. If t in u(t) is equal or greater than zero then u(t) equals 1.

    Remember the definition of a step signal.
     
  3. Xufyan

    Thread Starter Member

    Aug 3, 2010
    114
    0
    i wanna solve it without putting a value for t,

    what my teacher did is , he simply draw those three signals and cancelled out the opposite signals , the remaining signal is the answer ! what the hell was that ???
    is that a way of solving a signal ?
    he said there is no mathematical approach to solve signals (btw we have just started signals n system and this was my 2nd lecture),
    i wonder how the hell there is no way to solve the above equation mathematically.
    there must be a way which my teacher doesn't aware about,

    can you draw the output waveform of this signal and approach of solving it without assigning a value of t ?
     
  4. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Yes, you can plot each u() component of x(t) individually and then sum them up.

    Assume the component u(t+1):

    set t+1=0 and solve for t

    t=-1

    Thus, at t=-1 the signal rises from 0 t 1 (step)

    Do the same for all u() components.
     
  5. Xufyan

    Thread Starter Member

    Aug 3, 2010
    114
    0
    i already did that as i mentioned in my first post , re-read the first post please.

    but how to solve further,
    after this step ??
    look at this,

    u(t+1) = (-1,1)
    -2ut = (0,-2)
    u(t-1) = (1,1)

    you said exactly what i've already posted.

    can i solve it like

    u(t+1) - 2u(t) + u(t-1)

    (-1,1) + (0,-2) + (1,1) = 0

    is this correct ? if not then how to solve it ?
     
  6. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Draw the three signals on the same sheet and sum them up.
     
  7. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    The three functions are not continuous over the region from t=-∞ to t=+∞ and cannot be summed as you propose.

    Your summation only holds true for either t<-1 or t>=1.
     
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