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The representation of Fourier series can be in case of Non-periodic signals too.Group of answer choicesCan not be determinedTrueNoneFalse

Question

The representation of Fourier series can be in case of Non-periodic signals too.

Group of answer choices

  • Can not be determined
  • True
  • None
  • False
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Solution

The statement provided relates to the applicability of Fourier series to non-periodic signals.

Analysis of the Statements:

  1. True: This would imply that Fourier series can indeed represent non-periodic signals.
  2. False: This would suggest that Fourier series cannot represent non-periodic signals.
  3. Can not be determined: This option implies uncertainty about the applicability of Fourier series to non-periodic signals.
  4. None: This option is ambiguous and does not provide a clear evaluation.

Explanation:

Fourier series is primarily used to analyze periodic functions. For non-periodic functions, the Fourier transform is typically used, rather than the Fourier series. However, a Fourier series can theoretically be constructed for a non-periodic function if we consider it over a finite interval, addressing it as a form of approximation.

Conclusion:

The most accurate answer in this context is False, as Fourier series are designed specifically for periodic signals, while non-periodic signals are better handled by Fourier transforms.

Final Answer:

False.

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