Discrete-time signals with different frequencies can be equal; this is one manifestation of aliasing and folded aliases. Determine which of the following discrete-time cosine signals are equal (i. e., plots of xi[n]versus n will be identical):

x_1[n] = cos (0.9pi n + 0.1pi)
x_2[n] = cos (-2.9pi n + 0.1pi)
x_3[n] = cos (5.1pi n - 0.1pi)
x_4[n] = cos (6.9pi n - 0.1pi)
x_5[n] = cos (-7.1pi n - 0.1pi)

Explanation:

Firstly, x_1 and x_2 must be reviewed together. Then, x_3, x_4 and x_5 must be reviewed together. Since the phase differences (+0.1π and -0.1π) are different.

1)

2)

Although the magnitude plot of is equal to the magnitude plots of , their phase plot of  is not equal to the phase plots of the .

Moreover, although the magnitude plots of are equal, their phase plot are not equal.

answer:

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explanation:

answer:

(b)

explanation: