Question

Consider the DT signal $x[n] = \begin{cases} n+1, & 0 \le n \le 7 \\ 0, & \text{otherwise} \end{cases}$ Now consider its 8-point DFT defined by $X[k] = \sum_{n=0}^{7} x[n]e^{-j\frac{\pi}{4}kn}$ Enter the DFT values in the boxes below. Enter all values to 3 significant figures; phases in radians. 1. X[0] Magnitude: Number Phase: Number 2. X[1] Magnitude: Number Phase: Number 3. X[3] Magnitude: Number Phase: Number 4. X[7] Magnitude: Number Phase: Number

          Consider the DT signal
$x[n] = \begin{cases} n+1, & 0 \le n \le 7 \\ 0, & \text{otherwise} \end{cases}$
Now consider its 8-point DFT defined by
$X[k] = \sum_{n=0}^{7} x[n]e^{-j\frac{\pi}{4}kn}$
Enter the DFT values in the boxes below. Enter all values to 3
significant figures; phases in radians.
1. X[0]
Magnitude: Number
Phase: Number
2. X[1]
Magnitude: Number
Phase: Number
3. X[3]
Magnitude: Number
Phase: Number
4. X[7]
Magnitude: Number
Phase: Number

Consider the DT signal
x[n] = n+1, 0 ≤ n ≤ 7
0, otherwise
Now consider its 8-point DFT defined by
X[k] = ∑n=0^7 x[n]e^-j(π)/(4)kn
Enter the DFT values in the boxes below. Enter all values to 3
significant figures; phases in radians.
1. X[0]
Magnitude: Number
Phase: Number
2. X[1]
Magnitude: Number
Phase: Number
3. X[3]
Magnitude: Number
Phase: Number
4. X[7]
Magnitude: Number
Phase: Number

Added by Patrick H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Abdul Khalad

Step 1

Since c[n] = 10 for all values of n except when 0 < n < 7, we can write x[n] = c[n] for 0 < n < 7. Therefore, x[n] = 10 for 0 < n < 7. Step 2: Calculate the values of jTkn for 0 ≤ k ≤ 7. Since we are given an 8-point DFT, we need to calculate jTkn for 0 ≤ k ≤ Show more…

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Consider the DT signal n+1, 0 < n < 7, c[n] = 10, otherwise. Now consider its 8-point DFT defined by jTkn = []x i=0x[n]e. Enter the DFT values in the boxes below. Enter all values to 3 significant figures; phases in radians. 1. X[0] Magnitude: Number Phase: Number 2. X[1] Magnitude: Number Phase: Number 3. X[3] Magnitude: Number Phase: Number 4. X[7] Magnitude: Number Phase: Number