The windowing function itself can distort your data towards a bias. Window correction factors are used to try and compensate for the effects of applying a window to data. To correct for amplitude or energy distortion, each spectral line of a windowed frequency spectrum are multiplied by a fixed factor. This factor is determined by the window type that was applied. Different window functions are available with different frequency response characteristics. Choosing an optimal window for a specific application requires knowledge of the signals involved, consideration of the frequency resolution, and the dynamic range requirements

The moving objects and blocks compute the moving statistics of streaming signals using one or both of the sliding window method and exponential weighting method. The sliding window method has a finite impulse response, while the exponential weighting method has an infinite impulse response. To analyze a statistic over a finite duration of data, use the sliding window method. The exponential weighting method requires fewer coefficients and is more suitable for embedded applications. The exponential weighting method has an infinite impulse response. The algorithm computes a set of weights, and applies these weights to the data samples recursively. As the age of the data increases, the magnitude of the weighting factor decreases exponentially and never reaches zero. In other words, the recent data has more influence on the statistic at the current sample than the older data. Due to the infinite impulse response, the algorithm requires fewer coefficients, making it more suitable for embedded applications.

The value of the forgetting factor determines the rate of change of the weighting factors. A forgetting factor of 0.9 gives more weight to the older data than does a forgetting factor of 0.1. To give more weight to the recent data, move the forgetting factor closer to 0. For detecting small shifts in rapidly varying data, a smaller value (below 0.5) is more suitable. A forgetting factor of 1.0 indicates infinite memory. All the previous samples are given an equal weight. The optimal value for the forgetting factor depends on the data stream. For a given data stream, to compute the optimal value for forgetting factor, see [1].

The two primary factors that describe a window function are:

Width of the main lobe (i.e., at what frequency bin is the power half that of the maximum response)

Attenuation of the side lobes (i.e., how far away down are the side lobes from the mainlobe). This tells you about the spectral leakage in the window.

Another not so frequently considered factor is the rate of attenuation of the sidelobes, i.e., how fast do the sidelobes die down.

The rectangular function has a very narrow main lobe, but the side lobes are quite high, at ~13 dB. Other filters have significantly fatter main lobes, but fare much better in the side lobe suppression. In the end, it's all a trade-off. You can't have both, you have to pick one.

So that said, your choice of window function is highly dependent on your specific needs. For instance, if you're trying to separate/identify two signals that are fairly close in frequency, but similar in strength, then you should choose the rectangular, because it will give you the best resolution.

On the other hand, if you're trying to do the same with two different strength signals with differing frequencies, you can easily see how energy from one can leak in through the high sidelobes. In this case, you wouldn't mind one of the fatter main lobes and would trade a slight loss in resolution to be able to estimate their powers more accurately.

In seismic and geophysics, it is common to use Slepian windows (or discrete prolate spheroidal wavefunctions, which are the eigenfunctions of a sinc kernel) to maximize the energy concentrated in the main lobe.

Sources:

https://dsp.stackexchange.com/questions/208/what-should-be-considered-when-selecting-a-windowing-function-when-smoothing-a-t

https://community.plm.automation.siemens.com/t5/Testing-Knowledge-Base/Window-Correction-Factors/ta-p/431775

http://www.electronicdesign.com/analog/choose-right-fft-window-function-when-evaluating-precision-adcs

https://www.mathworks.com/help/dsp/ug/sliding-window-method-and-exponential-weighting-method.html

http://web.mit.edu/xiphmont/Public/windows.pdf

You need a windowing function, because spectral estimation methods, such as the FFT, assume that the waveform is observed from minus infinity to plus infinity where, in fact, it is multiplied by a rectangular wave, which has a width equal to the observation interval, a value of zero outside this, and a value of 1 within the interval. This means that the naively calculated spectrum will contain the spectral components of both. The usual window functions, which are easy to calculate, are the Hamming, Hanning and Blackman filters. A free tool, which might help you view results produced by all these functions on test (ASCII) data is available at www.designsim.com.au/dnlds/lvspice3 for a Linux version or www.designsim.com.au/dnlds/vspice3 for Sun SPARC

It may be a little late, but here are some examples of the effects of windowing on the FFT of a (not very clean) square wave.

The first image is a raw FFT. Notice the spurious ripples around each spectral line.

The second image uses a Hamming window on the same data. The ripples have been almost suppressed, and there is slight broadening of each spectral line

The third image uses a Hanning window. The ripples aren't suppressed as completely, but the broadening of spectral lines is slightly worse.

Finally, a Blackman window gives the best suppression, but causes the worst broadening of each spectral line.