Let $$X\left( {{e^{j\omega }}} \right) = \sum\nolimits_{n = - \infty }^\infty {x\left[ n \right]{e^{ - j\omega n}}} $$ and $$x\left[ n \right] = \frac{1}{{2\pi }}\int\limits_{ - \pi }^\pi {X\left( {{e^{j\omega }}} \right){e^{j\omega n}}d\omega } .$$
If $$X\left( {{e^{j\omega }}} \right) = \frac{1}{{\left( {1 - 0.2{e^{ - j\omega }}} \right)\left( {1 - 0.1{e^{ - j\omega }}} \right)}},$$ what is x[n] in terms of unit discrete step function u(n)?
A. 2(0.2)n u(n) - (0.1)n u(n)
B. 2(0.1)n u(n) - (0.2)n u(n)
C. (0.2)n u(n) - (0.1)n u(n)
D. (0.1)n u(n) - (0.2)n u(n)
Answer: Option A
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
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