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tritical · 30th November 2007, 03:14

I guess I'll try to give an explanation of some of the differences between the windows. There are basically three main characteristics to look at... the main lobe width, the peak side lobe level, and the side lobe roll off.

A small main lobe width gives better resolution. That is, given two equal magnitude peaks in the frequency spectrum, the smaller the main lobe width, the closer together the two peaks can be and we will still be able to resolve them. The rectangular window has the smallest main lobe width.

A small peak side lobe level makes it possible to resolve a weak (small) peak that is next to a, relatively speaking, strong (large) peak. The peak side lobe level determines the maximum response outside the main lobe. In other words, if the peak side lobe level is too high, then the energy from a strong peak can leak into nearby frequency bins and cover up a smaller peak if one is present. Of the windows implemented in dfttest, flat top or 7-term blackman-harris has the smallest peak side lobe level. The rectangular window has the largest peak side lobe level.

The third characteristic is the side lobe roll off, which gives the rate of decrease in the peak of each side lobe as you move away from the main lobe. Sometimes trading a faster roll off for a larger peak side lobe level (the peak side lobe level generally occurs in the side lobes closest to the main lobe) is good if there are no nearby peaks, but there are some farther away.

Thus, the best window would have a small main lobe width, a small side peak, and a fast roll off. The problem is that you can't have all of that at the same time. Generally, the smaller the main lobe width, the higher the side peak and vice versa. Of the windows in dfttest, the order from smallest to largest in terms of main lobe width is:

rectangular
bartlett
hamming
hanning
bartlett-hann
blackman
blackman-harris (4-term)
blackman-nutall
nutall
blackman-harris (7-term)
flat top

I left out kaiser-bessel because it is adjustable and could end up anywhere in there.

Exactly which window is best for denoising is hard to say, and would also depend on overlap amount, window size, etc... I can say from my tests in the objective denoiser thread that hanning/hamming with large overlap >= 75% and window size around 8-16 seemed to work best for removal of gaussian white noise (in terms of resulting psnr and ssim).

http://en.wikipedia.org/wiki/Image:W...parsion%29.png

This graph from wikipedia has pretty much all of the windows listed above, and shows the main lobe, along with the frequency envelope (you can see the peak side lobe level and how fast the roll off is).

30th November 2007, 03:14	#11 \| Link
tritical Registered User Join Date: Dec 2003 Location: MO, US Posts: 999	I guess I'll try to give an explanation of some of the differences between the windows. There are basically three main characteristics to look at... the main lobe width, the peak side lobe level, and the side lobe roll off. A small main lobe width gives better resolution. That is, given two equal magnitude peaks in the frequency spectrum, the smaller the main lobe width, the closer together the two peaks can be and we will still be able to resolve them. The rectangular window has the smallest main lobe width. A small peak side lobe level makes it possible to resolve a weak (small) peak that is next to a, relatively speaking, strong (large) peak. The peak side lobe level determines the maximum response outside the main lobe. In other words, if the peak side lobe level is too high, then the energy from a strong peak can leak into nearby frequency bins and cover up a smaller peak if one is present. Of the windows implemented in dfttest, flat top or 7-term blackman-harris has the smallest peak side lobe level. The rectangular window has the largest peak side lobe level. The third characteristic is the side lobe roll off, which gives the rate of decrease in the peak of each side lobe as you move away from the main lobe. Sometimes trading a faster roll off for a larger peak side lobe level (the peak side lobe level generally occurs in the side lobes closest to the main lobe) is good if there are no nearby peaks, but there are some farther away. Thus, the best window would have a small main lobe width, a small side peak, and a fast roll off. The problem is that you can't have all of that at the same time. Generally, the smaller the main lobe width, the higher the side peak and vice versa. Of the windows in dfttest, the order from smallest to largest in terms of main lobe width is: rectangular bartlett hamming hanning bartlett-hann blackman blackman-harris (4-term) blackman-nutall nutall blackman-harris (7-term) flat top I left out kaiser-bessel because it is adjustable and could end up anywhere in there. Exactly which window is best for denoising is hard to say, and would also depend on overlap amount, window size, etc... I can say from my tests in the objective denoiser thread that hanning/hamming with large overlap >= 75% and window size around 8-16 seemed to work best for removal of gaussian white noise (in terms of resulting psnr and ssim). http://en.wikipedia.org/wiki/Image:W...parsion%29.png This graph from wikipedia has pretty much all of the windows listed above, and shows the main lobe, along with the frequency envelope (you can see the peak side lobe level and how fast the roll off is).