The N-point DFT X of a sequence x[n] 0 ≤ n ≤ N − 1 is given by $$X\left[ k \right] = {1 \over {\sqrt N }}\,\,\sum\limits_{n = 0}^{N - 1} x \,[n\,]e{\,^{ - j{{2\pi } \over N}nk}}$$, 0$$ \le k \le N - 1$$ Denote this relation as X = DFT(x). For N= 4 which one of the following sequences satisfies DFT (DFT(x) ) = ___________.

x = $$\left[ {1\,2\,3\,2} \right]$$

x = $$\left[ {1\,2\,3\,4} \right]$$

x = $$\left[ {1\,2\,3\,2} \right]$$

x = $$\left[ {1\,3\,2\,2} \right]$$

x = $$\left[ {1\,2\,2\,3} \right]$$

GATE 2014 Electronics & Communication PYQ — Signals and Systems

GATE 2014Set 4PYQMCQanswer keyexplanation soonmedium

Signals and Systems · Sampling & DTFT

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Recurring concept

Sampling & DTFT has appeared in GATE Electronics & Communication 49 times across 28 years (2021, 2022, 2023, 2024, 2025, ...).