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4

I've done that. Used a flat-top window to estimate the amplitude. Then used a (fftshift'ed) Blackman-Nutall window to estimate the phase. That particular combination gave me a better pair of estimates than using a single, say, von Hann windowed FFT. Even with interpolation of the FFT results. Other combinations might work better for other purposes. The ...


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That makes little sense; the FFT (which is just an implementation of the DFT) is a linear operation; summing/weightedly averaging the same signal windowed with different windows is mathematically identical to just windowing with the summed/weightedly averaged window to begin with. It's literally the same. So, what you really want is to design / choose a ...


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Computing several versions in a family of transformations from the same data can be seen as an instance of "diversity enhancement". One may expect from it that interesting features may pop-up better and align, while uninformative ones will appear less coherent, so that a clever (often nonlinear) combination of the different "transformed ...


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Depending on the window function, you may be able to use a DFT-even version of the window function. "DFT-even" means that the periodic extension of the window function is symmetrical. In MATLAB and Octave you can get such a window like this (the first line in the source code): a = hanning(10, "periodic"); b = fftshift(a); c = a + b; plot(...


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Compute-expense: recordings may be tens if not hundreds of thousands of samples long with multiple channels. One either runs out of memory, or heavily downsamples at layer 1, which loses too much information before the NN can do much with it. Data augmentation: for e.g. classification, if you have a 10 minute segment belonging to same class, splitting it in ...


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Basically, to perform a spectral analysis. Take a look to this: http://support.ircam.fr/docs/AudioSculpt/3.0/co/Window%20Size.html I do not know if you refer to some specific approach, but usually, the main EEG classification approaches use frequency analysis (also combined with temporal analysis) to extract the features that will be used to train the ...


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SUMMARY The equivalent noise bandwidth (ENBW) for a window function is the bandwidth in bins of a brickwall filter that would result in the same noise power from a white noise source as the DFT "filter" (when viewing, appropriately, each bin of the DFT as a bandpass filter). The ENBW for the rectangular window (no further windowing) is 1 bin as ...


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A window function $w(t)$ satisfies $w(t)\ge 0$. The value of a window's frequency response $W(f)$ at DC ($f=0$) equals its integral $$W(0)=\int_{-\infty}^{\infty}w(t)dt>0\tag{1}$$ which is clearly greater than zero because $w(t)\ge 0$. For all other frequencies we obtain the following bound: $$|W(f)|=\left|\int_{-\infty}^{\infty}w(t)e^{-j2\pi ft}dt\right|\...


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You can see how it falls out if you work through the simple case of N=2 (I've elided the 1/N for brevity) \begin{equation} \frac{(Y_{1}X_{1}^{*}+Y_{2}X_{2}^{*})(X_{1}Y_{1}^{*}+X_{2}Y_{2}^{*})} {(X_{1}X_{1}^{*}+X_{2}X_{2}^{*})(Y_{1}Y_{1}^{*}+Y_{2}Y_{2}^{*})} \end{equation} It should be pretty obvious that there are now some cross products. Multiplying through:...


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