GATE 2016 EE (EE2) – Question 15
Signals and Systems · Fourier series representation of continuous and discrete time periodic signals, Sampling theorem · 1 mark · Numerical answer
A bandlimited signal x(t) has highest frequency 5 kHz. The highest frequency in $x(t)\cos(2000\pi t)$, in kHz, is ________.
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Correct answer: 6.0 to 6.0
Explanation
The cosine frequency is 2000π/(2π)=1000 Hz=1 kHz. Multiplication by a cosine shifts copies of the baseband spectrum to ±1 kHz.
The positive-frequency copy extends to 5+1=6 kHz, with the negative copy mirrored. Thus the highest frequency magnitude is **6 kHz**.
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