EE 3054: Signals, Systems, and Transforms
Fall 2011
Test 2•No notes, closed book.•Show your work.
•
Simplify your answers.
1. A continuous-time system is described by the equation,y(t) =12Ztt-2(x(τ))2dτwherexis the input signal,ythe output signal.Find the output signal ofthe system when the input signal is1-10125tx(t)2. Classify the system in the previous problem as:
(a) linear/nonlinear
(b) time-invariant/time-varying
(c) stable/unstable
(d) causa/non-causal
3. Find and sketch the convolution ofg(t) = e-2tu(t)and1tf(t)
0
1
2
3
4
5
4. A causal continuous-time LTI system is described by the equationy00(t) + 4y0(t) + 5y(t) =x0(t) + 2x(t)wherexis the input signal, andyis the output signal.(a) Find the impulse response of the system.(b) Accurately sketch the pole-zero diagram.(c) What is the dc gain of the system?(d) Classify the system as either stable or unstable.5. A causal continuous-time LTI system is described by the equationy00(t) + 4y0(t) + 5y(t) =A x00(t) +B x0(t) +C x(t)wherexis the input signal, andyis the output signal.Find constantsA, B, Cso that the system both annihilates 5 Hz tones andhas unity dc gain.6. Consider a continuous-time LTI system with the impulse response

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