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 in hertz of LPF(Low-Pass Filter)?}\,\! $
- See the solution here.
