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(ELEC211)[2008](sum)midterm1~ee_wxx^_10299.pdf
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ELEC.211.Mid\Term.1...Summer.2008..Duration:.1.hour.
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1.
.(20.Points).(Classifications.of.signals.and.systems)..Determine.if.the.following.system.is.linear,.time\invariant,.stable,.causal.and.invertible...



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(10.Points).Provide.Yes/No.answer..Correct.answer.will.get.2.points,.incorrect.answer.will.deduct.2.points,.no.answer.will.get.0.point..
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(10.Points).Provide.the.proof,.counter.example.or.explanation.to.support.your.Yes/No.answer..
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LINEAR.
TIME\INVARIANT.
STABLE.
CAUSAL.
INVERTIBLE.

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2.
(20.Points).(FS.properties)..


a.
(10.Points).Let.y(t).be.periodic.with.period.T.and.the.FS.coefficients.of.y(t).be and.let.the.signal.z(t).=.3.+.y(t).+.y(t/2)..Find.the.period.of.z(t) and.then.the.FS.coefficients.of.this.periodic.signal.z(t).in.terms.of.an..



b.
(10.Points).x(t).is.a.periodic.signal.with.FS.coefficients.of.bn.and.L;5.0,.which.of.the.following.CANNOT.be.x(t).and.why?.





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3..(20.Points).(Convolution.and.LTI.properties).
a..(10.Points).Sketch.the.result.
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b.
(10.Points).If(t).is.the.impulse.response.of.the.system.that.inverts.the.system.with.impulse.response.h1(t)..Find.the.equivalent.impulse.response.of.the.following.system...



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4.
(20.Points).(FS.and.Frequency.respof.syste

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e.oLTI.m)..a. (10.Points).If.x(t).=.1.+.2.cos(2t.+./4).+.3sin(4t.+./3), find.the.period.and.the.FS.coefficients.of.x(t)..


b.
(10.Points).If.we.input.the.above.signal.x(t).into.a.LTI.system.with.impulse.response.h(t).=.u(t)...u(t...0.5),.or.equivalently.frequency.response..


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Find.the.FS.coefficients.of.the.output.of.the.system..



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