The unit sample response of a discrete system is 1, $$\frac{1}{2},\,\frac{1}{4},$$ 0, 0, 0 . . . For an input sequence 1, 0, 1, 0, 0, 0 . . ., what is the output sequence?
A. $$1,\,\frac{1}{2},\,\frac{1}{4},\,\frac{1}{2},\,\frac{1}{4},\,0,\,0\,...$$
B. $$1,0,\,\frac{1}{4},\,0,\,0\,...$$
C. $$2,\,\frac{1}{2},\,\frac{5}{4},\,0,\,0\,...$$
D. $$1,\,\frac{1}{2},\,\frac{5}{4},\,\frac{1}{2},\,\frac{1}{4},\,0,\,0\,...$$
Answer: Option D

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