Question: Determine a sequence x[n] that satisfies all of the following three conditions: Condition 1: The Fourier transform of x[n] has the form X(e j? )

Determine a sequence x[n] that satisfies all of the following three conditions: Condition 1: The Fourier transform of x[n] has the form

X(e^j?) = 1 + A₁ cos ? + A₂ cos 2?,

Where A₁ and A₂ are some unknown constants.?

Condition 2: The sequence x[n]*?[n ? 3] evaluated at n = 2 is 5.

Condition 3: For the three-point sequence w[n] shown in Figure, the result of the eight-point circular convolution of w[n] and x[n ? 3] is 11 when n = 2; i.e.,

Ew[m]x[((n - 3 m))8]| = 11. In=2 m=0 3.

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