20115ee102_1_hw2

20115ee102_1_hw2 - x ( t ) and returns the even part of x (...

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1 EE102 Systems and Signals Fall Quarter 2011 Jin Hyung Lee Homework #2 Due: Wednesday, Oct 12, 2011 at 5 PM. 1. State whether the following systems are linear or nonlinear; time invariant or time variant; and why. (a) y ( t ) = x ( t ) sin( ωt + φ ) (b) y ( t ) = x ( t ) x ( t - 1) (c) y ( t ) = 1 + x ( t ) (d) y ( t ) = cos( ωt + x ( t )) (e) y ( t ) = Z t -∞ x ( τ ) (f) y ( t ) = Z t/ 2 -∞ x ( τ ) 2. A periodic signal x ( t ) , with a period T , is applied to a linear, time-invariant system H . Show that the output y ( t ) y ( t ) = H ( x ( t )) is also periodic, with period T . 3. Sample and hold system. A sample and hold (S/H) system, with sample time h , is described by y ( t ) = x ( h b t/h c ) , where b a c denotes the largest integer that is less than or equal to a . Sketch an input and corresponding output signal for a S/H, to illustrate that you under- stand what it does. Is a S/H system linear? 4. Consider a system that takes a signal

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Unformatted text preview: x ( t ) and returns the even part of x ( t ) as its output x e ( t ) = H ( x ( t )) where x e ( t ) is the even part of x ( t ) . Is this system linear? Is it time invariant? 2 5. System Equations from Block Diagrams Find the differential equation that correspond to this block diagram. Hint: Label all of the intermediate signals, and write equations for each. + y--+ x + + b a 6. It is often useful to represent operations on signals as convolutions. For each of the follow-ing, nd a function h ( t ) such that y ( t ) = ( x * h )( t ) . (a) y ( t ) = Z t- x ( ) d (b) y ( t ) = Z t t-T x ( ) d (c) y ( t ) = x ( t ) (d) y ( t ) = x ( t-1)...
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20115ee102_1_hw2 - x ( t ) and returns the even part of x (...

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