Q2: sampling an 8-point x(n) time-sequence and you want to sample "exactly three cycles" of a continuous x(t) sinusoid. The 8-point DFT output, x(m), is depicted in Figure 1. a): Given that sample rate was 4000Hz for x(n), calculate the magnitude response of Ix(3)], and phase response of x(3), and then write the time-domain equation for the discrete x(n) sinusoid in trigonometric form. Justify your answer. Hint: x(n) = Ao cos(2лfnts + 9) Ao = (2 M₂) ÷ N

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а
5-657
0 1 2 3 4 5 6 7
5.657
Real part of (x(n))
-5.657
Zmaginary part of 2 (m)
0 1 2 3 4 5 6 7
Transcribed Image Text:а 5-657 0 1 2 3 4 5 6 7 5.657 Real part of (x(n)) -5.657 Zmaginary part of 2 (m) 0 1 2 3 4 5 6 7
Q2: sampling an 8-point x(n) time-sequence and you want to sample "exactly three cycles"
of a continuous x(t) sinusoid. The 8-point DFT output, x(m), is depicted in Figure 1.
a):
Given that sample rate was 4000Hz for x(n), calculate the magnitude response of Ix(3)], and
phase response of x(3), and then write the time-domain equation for the discrete x(n) sinusoid
in trigonometric form. Justify your answer.
Hint: x(n) = Ao cos(2лfnts + 9)
Ao = (2 M₂) ÷ N
Transcribed Image Text:Q2: sampling an 8-point x(n) time-sequence and you want to sample "exactly three cycles" of a continuous x(t) sinusoid. The 8-point DFT output, x(m), is depicted in Figure 1. a): Given that sample rate was 4000Hz for x(n), calculate the magnitude response of Ix(3)], and phase response of x(3), and then write the time-domain equation for the discrete x(n) sinusoid in trigonometric form. Justify your answer. Hint: x(n) = Ao cos(2лfnts + 9) Ao = (2 M₂) ÷ N
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