GATE 2016 EC (EC3) – Question 18
Networks, Signals and Systems · Discrete-time Signals · 1 mark · Multiple choice
The signal $x[n]=\delta[n-3]+2\delta[n-5]$ has z-transform X(z). If $Y(z)=X(-z)$ is the transform of y[n], then
- $y[n]=x[n]$
- $y[n]=x[-n]$
- $y[n]=-x[n]$
- $y[n]=-x[-n]$
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Show answer and explanation
Correct answer: (C) $y[n]=-x[n]$
Explanation
The z-transform substitution z→−z corresponds to multiplying the sequence by $(-1)^n$. This signal is nonzero only at odd indices 3 and 5.
At both indices $(-1)^n=-1$, so every nonzero sample reverses sign without changing its time index. Hence **y[n]=−x[n], C**.
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