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A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos(200πt) at sampling instants t = n/400, n = 0,1, ... , 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined as

Which one of the following statements is true?
  • a)
    Only X[ 2] and X [6 ] are non-zero 
  • b)
    Only X [3 ] and X [5 ] are non-zero 
  • c)
    All X [k ] are non-zero
  • d)
    Only X [4 ] is non-zero
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A finite duration discrete-time signal x[n] is obtained by sampling th...
x(t) = cos 200πt




Suppose, 
Now, as we know,
If for {a, b , c, d} { A B, C, D}
Then for {a, 0, b, 0, c, 0, d, 0}  { A B, C, D, A, B, C, D}
Similarly, for y ( n ) = {1, - 1 , 1 , - 1 }   Y(k) = {0, 0, 4, 0} 
Here, for x{n) = {1, 0, -1, 0, 1, 0, -1, 0}
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A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos(200πt) at sampling instants t = n/400, n = 0,1, ... , 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined asWhich one of the following statements is true?a)Only X[ 2] and X [6 ] are non-zerob)Only X [3 ] and X [5 ] are non-zeroc)All X [k ] are non-zerod)Only X [4 ] is non-zeroCorrect answer is option 'A'. Can you explain this answer?
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A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos(200πt) at sampling instants t = n/400, n = 0,1, ... , 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined asWhich one of the following statements is true?a)Only X[ 2] and X [6 ] are non-zerob)Only X [3 ] and X [5 ] are non-zeroc)All X [k ] are non-zerod)Only X [4 ] is non-zeroCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos(200πt) at sampling instants t = n/400, n = 0,1, ... , 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined asWhich one of the following statements is true?a)Only X[ 2] and X [6 ] are non-zerob)Only X [3 ] and X [5 ] are non-zeroc)All X [k ] are non-zerod)Only X [4 ] is non-zeroCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos(200πt) at sampling instants t = n/400, n = 0,1, ... , 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined asWhich one of the following statements is true?a)Only X[ 2] and X [6 ] are non-zerob)Only X [3 ] and X [5 ] are non-zeroc)All X [k ] are non-zerod)Only X [4 ] is non-zeroCorrect answer is option 'A'. Can you explain this answer?.
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