Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [window-functions]

In signal processing, a window function is a mathematical function that is zero-valued outside of some chosen interval.

For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window, which describes the shape of its graphical representation. When another function or a signal (data) is multiplied by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap; the "view through the window". Applications of window functions include spectral analysis, filter design, and beamforming.

Source: Window function

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What should be considered when selecting a windowing function when smoothing a time series?

If one wants to smooth a time series using a window function such as Hanning, Hamming, Blackman etc., what are the considerations for favouring any one window over another?
babelproofreader
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FFT with asymmetric windowing?

Common non-rectangular window functions all seem to be symmetric. Is there ever a case when one would want to use a non-symmetric window function before an FFT? (Say if the data on one side of the FFT aperture were considered a bit more important…
hotpaw2
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Why do we use window in time domain rather than do FFT modify the spectrum and than inverse FFT

I thought that DSP would be done by using FFT of portions of a signal, modify the samples that result from FFT (since they represent the spectrum of our signal + noise) and remove any unwanted signals and than do an inverse FFT to get a time domain…
quantum231
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Is it customary to correct for the gain of a window?

Consider how the Hanning window is defined: 0.5 - 0.5 * cos(n*2*Pi/(N-1)) By this definition, it has a gain of 0.5, which is simply the average value of the coefficients. By contrast, Flattop windows, as defined, have unity gain, presumably by…
user5108_Dan
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Why would one use a Hann or Bartlett window?

Suppose we're designing a low-pass FIR filter, and I want to use one of these three windows: Bartlett, Hann or Hamming. From Oppenheim & Schafer's Discrete-Time Signal Processing, 2nd Ed, p. 471:} All three of them provide the same transition…
Tendero
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Effect of windowing on noise

I understand that truncating a signal in time 'smears' the frequency response depending on the window chosen. In general, the shorter the signal duration, the more 'flattened' the frequency response, as seen in The Fourier Transform of the Box…
abc
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Is the discrete Gaussian kernel an eigenfunction of the DFT?

So the Gaussian function is an eigenfunction of the Fourier transform because it transforms into itself, right? But this isn't true for the sampled Gaussian in the DFT because the tails of the function are truncated, right? Wikipedia describes a…
endolith
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A few questions about Slepian and generalized gaussian windows

I'm trying to add documentation for all the window functions in scipy.signal, and I'm stuck on the Slepian (same as DPSS?) and Generalized Gaussian windows, which I'd never heard of before. There are two variables that are shape parameters of some…
endolith
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What is a good FFT window function to reject DC?

I'm using an FFT to analyze what is essentially the power envelope of a signal (see here for info on the containing project), and, since power numbers are always positive, to eliminate the DC component I'd like to use a window function that is 50/50…
Daniel R Hicks
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How do I apply a function window to a signal?

How can I apply a window function like Hamming or Lanczos to a signal, using its coefficients? I mean, which method can I use to do this? FFT? Convolution? Which method has the better performance?
walteram
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Fourier transform artifacts

My starting point in what follows is a radially symmetric random field. Taking the Fourier transform of this (and plotting it in logarithm to highlight the patterns), I obtain the following image in Fourier space: As you can see, there is a…
user1991
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Does windowing affect Parseval's theorem?

I have computed Fourier transform from ecg data.It does obey Parseval's theorem, relation $$\sum_{n=0}^{N-1} \Big| x[n] \Big|^2 = \frac{1}{N} \sum_{k=0}^{N-1} \Big| X[k] \Big|^2$$ is fulfiled. But after I use window function…
wiedzminYo
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Is spectral leakage due to windowing 'different' for the DTFT and DFT?

I'm currently trying to improve my foundational understanding of spectral leakage due to windowing. The more I have been reading about it, the more I'm starting to think that 'windowing spectral leakage' can mean two completely different things…
Izzo
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Why are there so many windowing functions?

Many windowing functions are listed here in the Mathematica documentation. I tried using a few to reduce leakage when computing a Discrete Fourier Transform. From what I could tell it made little difference which windowing function is used. Two of…
Ted Ersek
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Proof that the rectangular window has the best resolution

The resolution of a window is typically defined by the width of its spectral mainlobe (3dB-width or null-to-null width). It is often stated that the rectangular window has the best resolution among all windows. In my work, I'd be looking for a…
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