(New page: Category:2010 Fall ECE 438 Boutin == Quiz Questions Pool for Week 12 == ---- Q1. Consider a causal FIR filter of length M = 2 with impulse response :<math>h[n]=\delta[n]-\delta[n-1]\,...) |
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Q1. Consider a causal FIR filter of length M = 2 with impulse response | Q1. Consider a causal FIR filter of length M = 2 with impulse response | ||
| − | :<math>h[n]=\delta[n] | + | :<math>h[n]=\delta[n]+\delta[n-1]\,\!</math> |
| − | a) Provide a closed-form expression for the | + | a) Provide a closed-form expression for the 9-pt DFT of <math>h[n]</math>, denoted <math>H_9[k]</math>, as a function of <math>k</math>. Simplify as much as possible. |
| − | b) Consider the sequence <math>x[n]</math> of length | + | b) Consider the sequence <math>x[n]</math> of length 9 below, |
| − | :<math>x[n]=\text{cos}(\pi n)(u[n]-u[n-8])\,\!</math> | + | :<math>x[n]=\text{cos}(\frac{1}{3}\pi n)(u[n]-u[n-8])\,\!</math> |
| − | <math> | + | <math>y_9[n]</math> is formed by computing <math>X_9[k]</math> as an 9-pt DFT of <math>x[n]</math>, <math>H_9[k]</math> as an 9-pt DFT of <math>h[n]</math>, and then <math>y_9[n]</math> as the 9-pt inverse DFT of <math>Y_9[k] = X_9[k]H_9[k]</math>. |
| − | Express the result <math> | + | Express the result <math>y_9[n]</math> as a weighted sum of finite-length sinewaves similar to how <math>x[n]</math> is written |
above. | above. | ||
Revision as of 01:45, 9 November 2010
Quiz Questions Pool for Week 12
Q1. Consider a causal FIR filter of length M = 2 with impulse response
- $ h[n]=\delta[n]+\delta[n-1]\,\! $
a) Provide a closed-form expression for the 9-pt DFT of $ h[n] $, denoted $ H_9[k] $, as a function of $ k $. Simplify as much as possible.
b) Consider the sequence $ x[n] $ of length 9 below,
- $ x[n]=\text{cos}(\frac{1}{3}\pi n)(u[n]-u[n-8])\,\! $
$ y_9[n] $ is formed by computing $ X_9[k] $ as an 9-pt DFT of $ x[n] $, $ H_9[k] $ as an 9-pt DFT of $ h[n] $, and then $ y_9[n] $ as the 9-pt inverse DFT of $ Y_9[k] = X_9[k]H_9[k] $.
Express the result $ y_9[n] $ as a weighted sum of finite-length sinewaves similar to how $ x[n] $ is written above.
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