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For x(n)={2 3 4 5 1 3}, plot the following Discrete Time signals.
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enter image description here

1) x(n-1)

Solution: $n’ = n-1 \\ \therefore n=n’-1$

n x(n) n’
-2 2 -3
-1 3 -2
0 4 -1
1 5 0
2 1 1
3 3 2

enter image description here

2) x(n)u(-n)

Solution: $n’ = -n \\ u[n] = 0, n\lt0 \\ = 1, n≥0$

n x(n) u(n’) x(n)u(-n)
-2 2 1 2
-1 3 1 3
0 4 1 4
1 5 0 0
2 1 0 0
3 3 0 0

enter image description here

3) x(n-1)u(-n-1)

Solution: $n’ = n-1 \\ ∴ n = n’+1$

enter image description here

4) x(-n)u(n)

Solution: n’ = -n

n n’ x(n’) u(n’) x(n’)u(n)
-2 2 2 1 2
-1 1 3 1 3
0 0 4 1 4
1 -1 5 0 0
2 -2 1 0 0
3 -3 3 0 0

enter image description here

Result: x(-n)u(n) = {4}

5) x(2n)

Solution: $n’ = 2n \\ \therefore n = n’/2$

n n’ x(n’)
-2 -1 2
-1 -1/2 3
0 0 4
1 1/2 5
2 1 1
3 3/2 3

enter image description here

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