Quiz Chapter 11.04: Discreet Fourier Transform

1. Given that W=e^{-i(2 \pi / N)}, where N=3. Then F=W^{N} can be computed as F=

2. Given that W=e^{-i(2 \pi / N)}, where N=3. Then F=W^{N/2} can be computed as F=

3. Given that N=2, \{ f \} = \begin{Bmatrix}4-6i\\-2+4i\end{Bmatrix}. The values for vector \{\widetilde{C}^{R}\} shown in

• • • \widetilde{C}_{n}^{R}=\displaystyle\sum_{k=0}^{N-1}\{f^{R}(k) \cos (\theta)+f^{I}(k) \sin (\theta)\}

can be computed as:

4. Given that N=2, \{ f \} = \begin{Bmatrix}4-6i\\-2+4i\end{Bmatrix}. The values for \{\widetilde{C}^{I}\} shown in Equation (22D)

• • • \widetilde{C}_{n}^{I}=\displaystyle\sum_{k=0}^{N-1}\{f^{I}(k) \cos (\theta)-f^{R}(k) \sin (\theta)\}

can be computed as:

5. The forcing function F(t) is given as:

• • • F(t) = \displaystyle\sum_{n=0}^{7} 10 \sin (2 \pi n t)

To avoid the aliasing phenomenon, the minimum number of sample data point N_{min} should be

6. Based on the figure below

aliasing phenomena will not occur because there were