GATE EC 2024 Set 1 — Question 59
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Signals & Systems → Discrete-Time Signals → DFT & FFT
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Question
The relationship between any -length sequence and its corresponding -point discrete Fourier transform is defined asAnother sequence is formed as below For the sequence , the value of is _______.
Correct answer
112 to 112
Solution
Given .
Using the duality property of the Discrete Fourier Transform (DFT):Applying this property twice to find :For the given sequence , the length .
Thus, .
The value is the DFT coefficient of the sequence , which is the sum of all elements in :Sum of .
Using the duality property of the Discrete Fourier Transform (DFT):Applying this property twice to find :For the given sequence , the length .
Thus, .
The value is the DFT coefficient of the sequence , which is the sum of all elements in :Sum of .
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