GATE EC 2023 Set 1 — Question 29
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Signals & Systems → Continuous-Time Signals → DFT & FFT
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Question
In the table shown below, match the signal type with its spectral characteristics.
| Signal type | Spectral characteristics |
|---|---|
| (i) Continuous, aperiodic | (a) Continuous, aperiodic |
| (ii) Continuous, periodic | (b) Continuous, periodic |
| (iii) Discrete, aperiodic | (c) Discrete, aperiodic |
| (iv) Discrete, periodic | (d) Discrete, periodic |
Correct answer
(B) (i) arrow (a), (ii) arrow (c), (iii) arrow (b), (iv) arrow (d)
Solution
The relationship between time-domain signals and their frequency-domain spectra follows these properties:
1.Continuous in time Aperiodic in frequency
2.Discrete in time Periodic in frequency
3.Aperiodic in time Continuous in frequency
4.Periodic in time Discrete in frequency
Matching based on these rules:- (i) Continuous, aperiodic signal Continuous, aperiodic spectrum (a)
- (ii) Continuous, periodic signal Discrete, aperiodic spectrum (c)
- (iii) Discrete, aperiodic signal Continuous, periodic spectrum (b)
- (iv) Discrete, periodic signal Discrete, periodic spectrum (d)
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