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Category: EE 113

Description

5/5 - (3 votes)

Problem 1. (15 points) Consider the following periodic signals x[n] and z[n], with period 3 each.

Can you relate the DTFS coefficients of x[n] with the DTFS coefficients of z[n]?

0

𝑥[𝑛] 1 1

0

𝑧[𝑛]

2

1 1

(Hint: Try to find a signal y[n] of period 3 such that z[n] = x[n] ~ y[n].)

Problem 2. (20 points) Determine the DTFTs of the following sequences:

(a). (10 points) x[n] =

1

2

n−3

u[n] +

1

3

n

u[n − 1].

(b). (10 points) x[n] =

1

4

n−1

u[n] + cos

π

3

n

.

Problem 3. (a). (10 points) Determine the IDTFT of the following:

X(Ω) = π

2

· rect

Ω

π

6

· e

−j2Ω

where we define the rectangular function rect(·) as

rect

Ω

Ωc

,

1, |Ω| < Ωc

0, Ωc ≤ |Ω| ≤ π

(b). (5 points) Determine the following quantity for the same signal x[n] in (a):

X∞

n=−∞

|x[n]|

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