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[[Category:2010 Fall ECE 438 Boutin]] | [[Category:2010 Fall ECE 438 Boutin]] | ||
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| + | [[Category:ECE438]] | ||
| + | [[Category:digital signal processing]] | ||
<span style="color:green"> Any comments and questions are welcome! </span> -[[User:han83|Jaemin]] | <span style="color:green"> Any comments and questions are welcome! </span> -[[User:han83|Jaemin]] | ||
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== Quiz Questions Pool for Week 5 == | == Quiz Questions Pool for Week 5 == | ||
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<math>\text{1. Find inverse Z-transform of } \frac{1}{1-az^{-1}} \text{ where } |z|<|a|. \,\!</math> | <math>\text{1. Find inverse Z-transform of } \frac{1}{1-az^{-1}} \text{ where } |z|<|a|. \,\!</math> | ||
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<math>\text{2. Find inverse Z-transform of } \frac{3z^{-3}}{1-az^{-1}} \text{ where } |z|<|a|. \,\!</math> | <math>\text{2. Find inverse Z-transform of } \frac{3z^{-3}}{1-az^{-1}} \text{ where } |z|<|a|. \,\!</math> | ||
| − | * If you use the time-shifting property of | + | * If you use the time-shifting property of Z-transform, it can be easily solved. See the details [[ECE438_Week5_Quiz_Q2sol|here]]. |
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<math>\text{3. Compute the Fourier series coefficients of the following signal:} \,\!</math> | <math>\text{3. Compute the Fourier series coefficients of the following signal:} \,\!</math> | ||
Latest revision as of 10:39, 11 November 2011
Any comments and questions are welcome! -Jaemin
Quiz Questions Pool for Week 5
$ \text{1. Find inverse Z-transform of } \frac{1}{1-az^{-1}} \text{ where } |z|<|a|. \,\! $
- This is solved in HW3. See the details at HW3 solution
$ \text{2. Find inverse Z-transform of } \frac{3z^{-3}}{1-az^{-1}} \text{ where } |z|<|a|. \,\! $
- If you use the time-shifting property of Z-transform, it can be easily solved. See the details here.
$ \text{3. Compute the Fourier series coefficients of the following signal:} \,\! $
$ x(t)=\left\{\begin{array}{ll}1&\text{ when } 0\leq t <1 \\ 0& \text{ when } 1\leq t <2\end{array} \right. \text{ and is periodic with the period of two.} $
- This was from one of the exercises. See the solution here.
$ \text{4. The rational Z-transform }H(z)\text{ has zero at } z_1=j\text{, and pole at }p_1=2, \,\! $
$ \text{which is expressed as }H(z)=\frac{z-z_1}{z-p_1}\text{. Compute the magnitude of }H(e^{jw})\text{ at }w_1=\frac{\pi}{2}, w_2=-\frac{\pi}{2} \,\! $
- See the solution here.
$ \text{Let } x(t)= \text{cos} 1000 \pi t + \text{sin} 1500 \pi t. \,\! $
$ \text{5. What is the Nyquist frequency of the signal } x(t)? \,\! $
$ \text{6. Suppose the sampling rate is }2000\text{Hz. Upsample the signal by a factor of }2\text{.} \,\! $
$ \text{In order to get rid of aliases, what is the cutoff frequency of digital LPF(Low-Pass Filter)?}\,\! $
- See the solution here.
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