# What is the energycorrection or amplitude correction for a Tukey window?

From this page: https://community.sw.siemens.com/s/article/window-correction-factors there is a list of correction factors for popular windows. Is there a correction factor for Tukey window, depending on factor for the Tukey-window? Have not found this as yet.

• that article assumes a specific implementation of a window (e.g., I've never used a Hann window where I needed to correct amplitude? What kind of definition do they use? Hann is just $\sin^2(\pi n/\text{length})$, how could amplitude become > 1?). Also, what kind of definition of "energy correction factor" do they use if the 1-amplitude uniform window has an energy factor of 1 instead of its length? Nov 8, 2022 at 9:29
• As far as I understood the articles they list, your amplitudes (for respective frequency bins) are either correct in energy or amplitude, never both at the same time. So depending on what you want to display or calculate, you need to correct the amplitudes. Nov 8, 2022 at 11:21
• I think the amplitude correction factor is also called effective bandwidth of the windowing function (f.ex. Hann Window = 1.5). In my case, I want to calculate the RMS amplitude of for a given frequency range. I need the amplitude correction factor for the window to include in the noise bandwidth factor. Nov 8, 2022 at 11:30

$$w$$ is the window function, $$N$$ is the length of the window.

• Amplitude correction: $$\text{ACF} = \cfrac{N}{\sum_{n=0}^{N-1}w[n]} = \cfrac{1}{\text{mean(w)}}$$

• Energy correction: $$\text{ECF} = \sqrt{\cfrac{N}{\sum_{n=0}^{N-1} w[n]^2}} = \cfrac{1}{\text{rms(w)}}$$

In matlab:

% Tukey
N = 2^16;
acf = 1/mean(tukeywin(N)); % = 1.3334
ecf = 1/rms(tukeywin(N)); % = 1.2061
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• Still something is a unclear: if i create an amplitude spectra by fft, what is the value without windowing and overlap. Is it the correct amplitude or energy? Nov 8, 2022 at 13:36
• then your window is effectively a rectangular window, so ACF = 1 and ECF = 1 as well.
– Jdip
Nov 8, 2022 at 13:48
• thanks, that makes sense. And then if I create the same with a window, what is the amplitude value? Is it just an uncorrected value and if i need either one, the correct energy or the correct amplitude, I need to apply them? Nov 8, 2022 at 13:53
• yes. It depends on the type of spectrum you are looking at. this in my opinion is the best reference on the subject.
– Jdip
Nov 8, 2022 at 14:02