GATE EC 2014 Set 4 — Question 29
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Signals & Systems → Discrete-Time Signals → DTFT & Properties
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Question
The sequence , where is the unit step sequence, is convolved with itself to obtain . Then is _______.
Correct answer
3.9 to 4.1
Solution
To find the sum of the values of the sequence , we can use the properties of the Discrete-Time Fourier Transform (DTFT).
1.Sum Property of DTFT:
The sum of the values of a sequence is equal to its DTFT evaluated at :2.DTFT of the input sequence:
Given , its DTFT is:3.Convolution Property:
Since , the DTFT of is the product of the DTFTs of the individual sequences:4.Evaluating the sum:
Alternatively, using the property that the sum of a convolution is the product of the sums:The final answer is 4.Continue learning with Success Tracker
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