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A finite duration sequence of length L is given as x(n) =1 for 0≤n≤L-1=0 otherwise , then what is the N point DFT of this sequence for N=L?
  • a)
    X(k) =L for k=0, 1,2….L-1
  • b)
    X(k) =L for k=0=0 for k=1,2….L-1
  • c)
    X(k) =L for k=0=1 for k=1,2….L-1
  • d)
    None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A finite duration sequence of length L is given as x(n) =1 for 0≤n&...
Explanation: The Fourier transform of this sequence is

If N=L, then X(k)= L for k=0
=0 for k=1,2….L-1
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Most Upvoted Answer
A finite duration sequence of length L is given as x(n) =1 for 0≤n&...
The given sequence can be expressed as:

x(n) = u(n) - u(n-L)

where u(n) is the unit step function defined as:

u(n) = 1 for n >= 0
u(n) = 0 for n < />

The first term u(n) represents the onset of the sequence at n=0, while the second term u(n-L) represents the end of the sequence at n=L-1. By subtracting these two terms, we obtain a sequence that is 1 for n between 0 and L-1, and 0 elsewhere.

This type of sequence is commonly known as a rectangular pulse, and is often used in signal processing and digital communications. It has a finite duration and a well-defined start and end time, making it useful for representing signals that occur over a specific time interval.
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A finite duration sequence of length L is given as x(n) =1 for 0≤n≤L-1=0 otherwise , then what is the N point DFT of this sequence for N=L?a)X(k) =L for k=0, 1,2….L-1b)X(k) =L for k=0=0 for k=1,2….L-1c)X(k) =L for k=0=1 for k=1,2….L-1d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?
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