GATE 2016 EC (EC3) – Question 16

Networks, Signals and Systems · Continuous-time Signals · 1 mark · Multiple choice

Let $x(t)=\cos(6\pi t)+\sin(8\pi t)$, with t in seconds. The Nyquist sampling rate in samples/s for $y(t)=x(2t+5)$ is

Show answer and explanation

Correct answer: (C) 16

Explanation

The original frequencies are 3 Hz and 4 Hz. Replacing t by 2t+5 doubles both frequencies to 6 Hz and 8 Hz; the constant shift changes phases only.

The highest frequency in y is therefore 8 Hz. Twice that value gives the Nyquist rate **16 samples/s, C**.

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