Problem 2-7
(3) Linear. Consider the responses to two arbitrary inputs:
' m) = an?)
yztr) = x202)
Multiply rst by a and the second by bland add to get
ayiU) + [73:20) = M102) + M202)
That is, for the input ax1(t)+ lax/2(1), we replace 1 by :2 to get t
P
-38 Ch. 1 / Signal and System Modeling Concepts
(b) For the trapezoidal integration rule given in recursive form in Example 1-3. show that the
nonrecursive form up through time NT is
5W7) = 5(0) + [0(0) + a(NT) + 2 a(n
Check this, using vaiues from
Problem 1-3
(a) The signal can be developed in terms of equations as follows:
_ 1, mm s 112
mu) * {0, otherwise
_ 1, |r| g 10:2 = 5
_ 0, otherwise
This is a rectangular pulse of amplitude 1 between -5 and 5 and 0 otherwise. A sketch will be given
at t