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Signal and systems miscellaneous

Signals and Systems

  1. The causal sequence f(n) if f(z) =
    1
    1 -
    1
    z-12
    2
    1. 1
      n+ n
      1
      nu[n]
      22
    2. 1
      n+
      n
      1
      nu[n]
      222
    3. 1
      n– n
      1
      nu[n]
      33
    4. 1
      n+ n
      1
      nu[n]
      33
Correct Option: B

We will apply same approach as discussed in above problem.

(A)
1
n+ n
1
n u(n)
22

1
n←z→
1
21 -
1
z-1
2

and n
1
n←z→
z-1
21 -
1
z-12
2

Now,
1
n+ n
1
n u(n)
22

=
1
+
z-1
1 -
1
z-11 -
1
z-12
2
2


=1 –
1
z– 1 + z– 1
2
1 –
1
z– 12
2


=1 +
1
z– 1
2
1 –
1
z– 12
2

Since, (A) is not the correct choice, so we will solve for next option, i.e., (B).
1
n+
n
1
nu[n]
222

1
+
z-1
1 -
1
z-121 -
1
z-12
2
2


1 –
1
z– 1+ z– 1
2
1 –
1
z– 12
2

2 – z– 1 + z– 1
21 -
1
z-12
2

2
21 -
1
z-12
2

1
1 -
1
z-12
2

Therefore, option (B) is the correct choice.



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