# HW2 - t = exp-2 t u t(b f t = tu t(exp(1-t-t u t-1(c f t =...

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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 f i ( t ) i = 1 ,..., 5 in the ﬁgure below using only f ( t ), and its time-shifted, time-scaled and time-inverted versions. For example f 2 ( 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 to one of the TAs, or leave it in my mailbox (in the EE oﬃce on the 13th ﬂoor of Mudd). 1

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Unformatted text preview: t ) = exp(-2 t ) u ( t ) (b) f ( t ) = tu ( t ) + (exp(1-t )-t ) u ( t-1) (c) f ( t ) = Re { exp((1 + 2 πj ) 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 f 2 ( t-3), 3 f 2 (2 t + 2) and f 2 (2 t-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) ± sin t t 3 +2 ² δ ( t ) (b) 5+ jt 2-jt δ ( t-2) (c) R ∞-∞ (2 t-5) δ ( t-2) dt (d) exp(3 k ) cos(401 πk ) δ ( k + 1) (e) R x +1-∞ (2 t-5) δ ( t-x ) dt (f) R ∞-∞ exp(3 x ) cos(401 πx ) δ ( x + 1) dx 2.6 - Find and sketch the even and odd components of f ( t ) = t ( u ( t + 1)-u ( t-2)) . 2...
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## This note was uploaded on 11/08/2011 for the course EE 111 taught by Professor Kim during the Spring '11 term at Korea University.

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HW2 - t = exp-2 t u t(b f t = tu t(exp(1-t-t u t-1(c f t =...

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