What does the exponential term mean in Fourier transform

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Discussion Overview

The discussion revolves around the meaning of the exponential term in the context of the Fourier Transform, specifically its relationship to Fourier series. Participants explore the theoretical implications and interpretations of this term.

Discussion Character

  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that the Fourier Transform involves an exponential term, exp^{-j w t}, and questions its meaning.
  • Another participant suggests that the exponential term is a complex generalization of sine and cosine functions, which are fundamental to Fourier series.
  • A later reply reiterates the connection to Fourier series, emphasizing the role of the exponential in the context of the interview question posed to them.

Areas of Agreement / Disagreement

Participants seem to agree on the connection between the exponential term and Fourier series, but the discussion does not reach a consensus on a deeper interpretation of the exponential term itself.

Contextual Notes

The discussion does not address potential limitations or assumptions regarding the definitions of the Fourier Transform or Fourier series.

ramdas
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We know that Fourier Transform F(W) of function f(t) is summation from -infinity to +infinity product of f(t) and exp^{-j w t}Here, what does the exponential term mean?
 
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Are you familiar with Fourier series? Because the exponential is simply the (complex) generalization of the sine and cosine that appears in the Fourier series.
 
DrClaude said:
Are you familiar with Fourier series? Because the exponential is simply the (complex) generalization of the sine and cosine that appears in the Fourier series.
sir,Question was asked to me at time of interview.
 
DrClaude said:
Are you familiar with Fourier series? Because the exponential is simply the (complex) generalization of the sine and cosine that appears in the Fourier series.
ramdas said:
sir,Question was asked to me at time of interview.
DrClaude didn't ask where the question came from. He asked whether you were familiar with Fourier series, and gave an explanation for the meaning of the exponential factor in the summation/integral.
 

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