Difference between revisions of "ECE438 Week5 Quiz" - Rhea

Revision as of 08:46, 19 September 2010

Now I am working on making pages of solutions. Thus, some of the solutions are not available right now. Those will be completed tonight! -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 in hertz of LPF(Low-Pass Filter)?}\,\! $

• See the solution here.

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