How can I normalize a window function for accurate Fourier transforms?

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SUMMARY

This discussion focuses on normalizing window functions to ensure accurate Fourier transforms, specifically addressing amplitude consistency in the output. The user experimented with various window functions and found that normalizing to RMS (Root Mean Square) effectively retained the amplitude of the Fourier transform. The initial approach of dividing by the integral was ineffective, highlighting the importance of proper normalization techniques in signal processing.

PREREQUISITES
  • Understanding of Fourier transforms and their applications
  • Familiarity with window functions in signal processing
  • Knowledge of RMS (Root Mean Square) calculations
  • Basic principles of signal normalization techniques
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  • Research different types of window functions and their properties
  • Learn about the mathematical formulation of RMS normalization
  • Explore the impact of windowing on Fourier transform results
  • Investigate advanced normalization techniques for signal processing
USEFUL FOR

Signal processing engineers, audio engineers, and anyone involved in Fourier analysis and window function applications will benefit from this discussion.

TheDestroyer
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Hello guys :)

I'm applying a window function to a signal before using a Fourier transform on it, but the problem is that the Fourier transform's amplitude (RMS or Volt/Sqrt(Hz)) is changing. Some windows are normalised to retain the amplitude. I'm making sure this is happening by Fourier transforming white noise before and after applying the window.

Could you guys tell me how to start with normalising a window? I tried simply dividing by the integral but it wasn't a good idea. I don't know where to start.

Thank you for any efforts :)
 
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I think normalising the Window to RMS did it. Thank you :)
 

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