The unit sample response of a discrete system is 1 1/2 1/4

The unit sample response of a discrete system is 1 1/2 1/4 0 0 0 … For an input sequence 1 0 10 0 0 … what is the output sequence?

1. 1 1/2 1/4 1/2 1/4 0 0 …
2. 1 0 1/4 0 0 … …
3. 2 1/2 5/4 1/2 1/4 0 0 …
4. 1 1/2 5/4 1/2 1/4 0 0 …

Given that,

h[n] = 1	1	1	0 0 0 ............
	2	4

x[n] = 1 0 1 0 0 0 ……
y(n) can be calculated by using method given below:

y[n] = 1	1		1 +	1		1	1	0 0 ............
	2			4		2	4

y[n] = 1	1	5	1	1	0 0 ............
y[n] = 1	2	4	2	4	0 0 ............

Hence, alternative (D) is the correct choice.