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

In summary, the speaker is having an issue with the amplitude of the Fourier transform changing when applying a window function to a signal. They are seeking advice on how to properly normalize the window and have found success with normalizing it to RMS.
  • #1
TheDestroyer
402
1
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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  • #2
I think normalising the Window to RMS did it. Thank you :)
 

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

What is a window function?

A window function is a mathematical function used in signal processing to modify a signal by reducing or amplifying certain parts of the signal. Commonly used window functions include rectangular, triangular, and Hamming windows.

Why is it important to normalise a window function?

Normalising a window function ensures that the total energy of the windowed signal remains constant regardless of the shape or size of the window. This is crucial in preserving the integrity of the signal and avoiding distortions.

How do you normalise a window function?

To normalise a window function, you need to divide the function by a normalisation constant, which is usually the sum of all the values in the window. This ensures that the total energy of the signal remains constant.

What are the benefits of normalising a window function?

Normalising a window function helps to reduce the effects of spectral leakage, which is the leakage of energy from one frequency bin to another. It also helps to improve the frequency resolution of the signal and reduce side lobes in the frequency spectrum.

Can normalising a window function affect the original signal?

Yes, normalising a window function can affect the original signal by altering its amplitude. However, the effects are usually minimal and necessary to ensure the integrity of the signal in signal processing applications.

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