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*Under construction --[[User:zhao148|Zhao]] | *Under construction --[[User:zhao148|Zhao]] | ||
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| − | Q1. | + | Q1. Consider the discrete-time signal |
| + | |||
| + | <math>x[n]=2\delta[n]+5 \delta[n-1]+\delta[n-1]- \delta[n-2].</math> | ||
| + | |||
| + | a) Determine the DTFT <math>X(\omega)</math> of x[n] and the DTFT of <math>Y(\omega)</math> of y[n]=x[-n]. | ||
| + | |||
| + | b) Using your result from part a), compute | ||
| + | |||
| + | <math>x[n]* y[n]</math>. | ||
| + | |||
| + | c) Consider the discrete-time signal | ||
| + | |||
| + | <math>z[n]=\left\{ \begin{array}{ll}x[(-n)\mod 4],& 0\leq n < 3,\\ 0 & \text{else }\end{array} \right. </math>. | ||
| + | |||
| + | Obtain the 4-point circular convolution of x[n] and z[n]. | ||
| + | |||
| + | d) When computing the N-point circular convolution of x[n] and the signal | ||
| + | |||
| + | <math>z[n]=\left\{ \begin{array}{ll}x[(-n)\mod N],& 0\leq n < N-1,\\ 0 & \text{else }\end{array} \right. </math>. | ||
| + | |||
| + | how should N be chosen to make sure that the result is the same as the usual convolution between x[n] and z[n]? | ||
* Same as HW8 Q3 available [[ECE438_HW8_Solution|here]]. | * Same as HW8 Q3 available [[ECE438_HW8_Solution|here]]. | ||
Revision as of 13:36, 16 November 2010
Quiz Questions Pool for Week 13
- Under construction --Zhao
Q1. Consider the discrete-time signal
$ x[n]=2\delta[n]+5 \delta[n-1]+\delta[n-1]- \delta[n-2]. $
a) Determine the DTFT $ X(\omega) $ of x[n] and the DTFT of $ Y(\omega) $ of y[n]=x[-n].
b) Using your result from part a), compute
$ x[n]* y[n] $.
c) Consider the discrete-time signal
$ z[n]=\left\{ \begin{array}{ll}x[(-n)\mod 4],& 0\leq n < 3,\\ 0 & \text{else }\end{array} \right. $.
Obtain the 4-point circular convolution of x[n] and z[n].
d) When computing the N-point circular convolution of x[n] and the signal
$ z[n]=\left\{ \begin{array}{ll}x[(-n)\mod N],& 0\leq n < N-1,\\ 0 & \text{else }\end{array} \right. $.
how should N be chosen to make sure that the result is the same as the usual convolution between x[n] and z[n]?
- Same as HW8 Q3 available here.
Q2.
Q3.
Q4.
Q5.
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