Evaluation of step functions

Discussion in 'Math' started by smarch, Nov 20, 2010.

  1. smarch

    Thread Starter Active Member

    Mar 14, 2009
    52
    0
    I am asked to evaluate this combination of step functions, though I have no idea what to do with it.
    Anyone have any information on these types of problems or know what to do with it?

    x(t) = t^2.u(t) - t^2.u(t-1) + (t-2)^2.u(t-1) - u(t-3)

    Thanks.
     
  2. smarch

    Thread Starter Active Member

    Mar 14, 2009
    52
    0
    anyone? please
     
  3. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    A step function equals to 1 for t>=0. Assign values to t and see at which part u(t-x)>=0.
     
  4. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    As mik3 said, make a timeline and for each time sample (step) evaluate your function x(t) at that point.
     
  5. someonesdad

    Senior Member

    Jul 7, 2009
    1,585
    141
    Here's a python program that will evaluate the function if you think it's too much trouble to make a plot by hand:

    Code ( (Unknown Language)):
    1.  
    2. from __future__ import division
    3. from pylab import *
    4.  
    5. def function(t):
    6.     u = lambda t: 1 if t >=0 else 0
    7.     return t**2*u(t) - t**2*u(t-1) + (t-2)**2*u(t-1) - u(t-3)
    8.  
    9. n, a = 1000, 4
    10. T, y = arange(-a, a, a/n), []
    11. for t in T:
    12.     y.append(function(t))
    13. plot(T, y)
    14. grid(True)
    15. show()
    16.  
    You'll need numpy and matplotlib to make the plot. u is the unit step function; there are different definitions floating around, so make sure you use the one your teacher wants you to use.
     
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