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X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation  
  • a)
    x(t)  = -x(t-T)
  • b)
    x(t) = -x(T-t) = -x(-t)
  • c)
    x(t) = x(T-t) = -x (t-T/2)
  • d)
    x(t) = x(t-T) = x(t-T/2)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
X(t) is a real valued function of a real variable with period T. Its t...
No sine terms are present.
∴ x(t) is even function.
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Community Answer
X(t) is a real valued function of a real variable with period T. Its t...
Ω = 0. This means that the expansion does not contain any terms of the form cos(0t) or sin(0t), which correspond to the constant term in the Fourier series. In other words, the function X(t) does not have a DC offset or a constant component in its Fourier series representation.
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X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation a)x(t) = -x(t-T)b)x(t) = -x(T-t) = -x(-t)c)x(t) = x(T-t) = -x (t-T/2)d)x(t) = x(t-T) = x(t-T/2)Correct answer is option 'D'. Can you explain this answer?
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X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation a)x(t) = -x(t-T)b)x(t) = -x(T-t) = -x(-t)c)x(t) = x(T-t) = -x (t-T/2)d)x(t) = x(t-T) = x(t-T/2)Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation a)x(t) = -x(t-T)b)x(t) = -x(T-t) = -x(-t)c)x(t) = x(T-t) = -x (t-T/2)d)x(t) = x(t-T) = x(t-T/2)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation a)x(t) = -x(t-T)b)x(t) = -x(T-t) = -x(-t)c)x(t) = x(T-t) = -x (t-T/2)d)x(t) = x(t-T) = x(t-T/2)Correct answer is option 'D'. Can you explain this answer?.
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