Prove FT^2(f(x))=f(-x): Answers & Tips

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SUMMARY

The discussion centers on proving the identity FT^2(f(x)) = f(-x) using the Fourier transform (FT). Participants emphasize the importance of recognizing that the integral involving the exponential functions is proportional to the delta function, specifically delta(t1 + t2). The necessity of considering even and odd functions is also highlighted, indicating that this distinction may simplify the proof process.

PREREQUISITES
  • Understanding of Fourier transform (FT) concepts
  • Familiarity with properties of even and odd functions
  • Knowledge of delta functions in mathematical analysis
  • Basic skills in integral calculus
NEXT STEPS
  • Study the properties of the Fourier transform in detail
  • Learn about the delta function and its applications in signal processing
  • Explore the implications of even and odd functions in Fourier analysis
  • Investigate integral techniques involving exponential functions
USEFUL FOR

Mathematicians, physicists, and engineering students focusing on signal processing and Fourier analysis will benefit from this discussion.

liorda
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Prove: [tex]FT^2(f(x))=f(-x)[/tex] where [tex]FT[/tex] is the Fourier transform.

I tried to change [tex]x[/tex] into [tex]-x'[/tex] but with no success.

Do I need to separate cases for even f and odd f?
 
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You just need to realize that e.g., integral(exp(i*k*t1)*exp(i*k*t2)*dk) is proportional to delta(t1+t2).
 

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