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(ELEC211)[2008](sum)midterm1~ee_wxx^_10298.pdf
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1..
.
a..
.
LINEAR.
TIME\INVARIANT
STABLE
CAUSAL
INVERTIBLE.
System..
No.
No.
No.
Yes.
Yes.
.
.
.
.
b..
.
Non\linear.
.
...
...
)()(tjatjx=ime.variant.
.T.
..
.
x.
.
Unstable.
.
y(t)...(unbounded).due.to.the.scaling.factor.(t.+.3)..when..t...
.
Causal.
.
y(t).does.not.depend.on.the.future.input..It.only.depends.on.the.current.x(t).and.the.past.x(t...3)..
.Invertible......jb
For.x(t).is.real.:.)(tx=:...
For.x(t).is.imaginary...
)()(ttx)3)3()(tty.For.x(t).is.complex.:..)()()(tjbtatx+=..(2)3())3()(atjbtty+.++=No.two.inputs.will.give.the.same.output.because.the.first.term.is.distinct.for.any...
.
2..
.
Consider.te.invertiI.system.:.
.
hble.LT.
..
.
....
.............
...
..
.
c.
b
)(32)(*)(tcbthtaB.y.comparison.:.Impulse.response.of.system.B.=.
.
.B.
.
..
3............
.
.
a
.
.
.
.
.
.
.
.
.
.
..b..........
.
x3(t).1.
1
1
..
4
....
...
a.
.....
.
....(real).
.
..
..
.b.
.
.
his.is.a.real.system.:..
.T.
.and..
.
.
.where...
.and.
.
.
.
.
.
5..
.
.