GATE EC 2024 Set 1 — Question 48
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Signals & Systems → Continuous-Time Signals → Filters & Bandwidth
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Question
A continuous time signal is sampled at a rate of Hz. The sampled signal when passed through an LTI system with impulse response produces an output . The expression for is _____.
Solution
Spectrum of the sampled signal. hasIdeal sampling at Hz giveswhich has lines at Hz: , each scaled by 15.The filter. has transform , an ideal low-pass filter with passband Hz. Since , multiplying by it shifts that passband to Hz:The passband is Hz.Output. Only the images at Hz () pass:Options A and C are the same signal. Using :So (A) and (C) both describe the output exactly.
- (B) : wrong phase.
- (D) : wrong sign of the phase.
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