GATE 2017 EE (EE2) – Question 42
A cascade has $h_1[n]=\{1,-1\}$ and $h_2[n]=\{1,1\}$. All sequences shown begin at n=0. Which input produces $y[n]=\{1,2,1,-1,-2,-1\}$?
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Correct answer: (D) $\{1,2,2,1\}$
Explanation
Convolving the two impulse responses gives h[n]={1,0,−1}. The cascade therefore obeys $y[n]=x[n]-x[n-2]$.
Starting at n=0 with zero samples before the origin: x0=y0=1, x1=y1=2, x2=y2+x0=2, and x3=y3+x1=1.
The next two output samples are −x2=−2 and −x3=−1, as required. Thus **x={1,2,2,1}, D**.