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Q2. Suppose that the LTI filter <math>h_1</math> satifies the following difference equation between input <math>x[n]</math> and output <math>y[n]</math>. | Q2. Suppose that the LTI filter <math>h_1</math> satifies the following difference equation between input <math>x[n]</math> and output <math>y[n]</math>. | ||
| − | <math> {\color{White}ab} y[n] = h_1[n]\;\ast\;x[n] = \frac{1}{4} y[n-1] + x[n] </math> | + | <math> {\color{White}ab} y[n] = h_1[n]\;\ast\;x[n] = \frac{1}{4} y[n-1] + x[n] </math> |
| + | |||
| + | (<math>\ast</math> implies the convolution) | ||
Then, find the inverse LTI filter <math>h_2</math> of <math>h_1</math>, which satisfies the following relationship for any discrete-time signal <math>x[n]</math>, | Then, find the inverse LTI filter <math>h_2</math> of <math>h_1</math>, which satisfies the following relationship for any discrete-time signal <math>x[n]</math>, | ||
Revision as of 19:11, 8 October 2010
Under construction -Jaemin
Quiz Questions Pool for Week 8
Q1. Find the impulse response of the following LTI systems and draw their block diagram.
(assume that the impulse response is causal and zero when $ n<0 $)
$ {\color{White}ab}\text{a)}{\color{White}abc}y[n] = 0.6 y[n-1] + 0.4 x[n] $
$ {\color{White}ab}\text{b)}{\color{White}abc}y[n] = y[n-1] + 0.25(x[n] - x[n-3]) $
Q2. Suppose that the LTI filter $ h_1 $ satifies the following difference equation between input $ x[n] $ and output $ y[n] $.
$ {\color{White}ab} y[n] = h_1[n]\;\ast\;x[n] = \frac{1}{4} y[n-1] + x[n] $
($ \ast $ implies the convolution)
Then, find the inverse LTI filter $ h_2 $ of $ h_1 $, which satisfies the following relationship for any discrete-time signal $ x[n] $,
(assume that the impulse responses are causal and zero when $ n<0 $)
$ {\color{White}ab} x[n] = h_2[n]\;\ast\;h_1[n]\;\ast\;x[n] $
$ \text{Q3.} $
$ \text{Q4.} $
$ \text{Q5.} $
$ \text{Q6.} $
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