- ELEN3801 Fall 2009 Homework 2
Due Thursday September 24th at the beginning of class (Mudd 227 9:10am)1 Carefully justify ALL your answers
2.1 - Find the energy of the signals sketched below. How does the energy change when transforming a signal by time-shifting or time-reversing it? How does the energy of a signal f (t) changes when it is multiplied by a factor a R.
2.2 - Express the signals fi (t) i = 1, . . . , 5 in the figure below using only f (t), and its time-shifted, time-scaled and time-inverted versions. For example f2 (t) = f (t - 1) + f (1 - t).
2.3 - Sketch the following signals, and state if these are causal, anti-causal, or non-causal.
1 You can always hand-in the homework earlier if you so desire - just give it to me or one to of the TAs, or leave it in my mailbox (in the EE office on the 13th floor of Mudd).
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(a) f (t) = exp(-2t)u(t) (b) f (t) = tu(t) + (exp(1 - t) - t)u(t - 1) (c) f (t) = Re{exp((1 + 2j)t)}u(1 - t) 2.4 - (a) - Express the signals in the figure below by a single expression valid for all t. (b) - Carefully sketch the signals f2 (t - 3), 3f2 (2t + 2) and f2 (2t - 1). (Note: the use of the step function u(t) will come in handy for the first part)
2.5 - Simplify the following expressions: (a) (c) (e)
sin t t3 +2 (t) (2t - 5)(t - 2)dt - x+1 (2t - 5)(t - x)dt -
(b)
5+jt 2-jt (t
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(d) exp(3k) cos(401k)(k + 1) (f) - exp(3x) cos(401x)(x + 1)dx
2.6 - Find and sketch the even and odd components of f (t) = t(u(t + 1) - u(t - 2)) .
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