The GATE Grind

GATE 2022 IN – Question 18

Signals and Systems · Fourier analysis and sampling · 1 mark · Multiple choice

The signal $x(t)$ is band-limited between 100 Hz and 200 Hz. If $y(t)=x(2t-5)$, which statement is always true?

  1. $y(t)$ is band-limited between 50 Hz and 100 Hz
  2. $y(t)$ is band-limited between 100 Hz and 200 Hz
  3. $y(t)$ is band-limited between 200 Hz and 400 Hz
  4. $y(t)$ is not band-limited

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Show answer and explanation

Correct answer: (C) $y(t)$ is band-limited between 200 Hz and 400 Hz

Explanation

The factor two in x(2t−5) doubles all spectral frequencies; translation contributes phase without changing support.

Thus the band becomes **200–400 Hz, C**.