DSP windows

admin: First posted on 2014 20 04

tictac, 2014 20 04: One thing I don't understand - there are all kinds of DSP windows in this site, but there is no discussion of whether one or another is better than the rest. Is there a standard way to measure the performance of windows? Thanks.

mic, 2014 23 04: There are some standard computations. The words that you should look for around the internet are: 1) highest sidelobe level; 2) sidelobe falloff; 3) coherent gain (e.g., the DC gain of the window, usually from the discrete Fourier transform); 4) processing gain; 5) scalloping gain (i.e., the maximum reduction in processing gain resulting from the frequency); 6) worst-case processing loss; 7) overlap correlation; 8) main lobe spectral response; 9) equivalent noise bandwidth, etc.

We are preparing to put some explanations of these in the wiki of this site and we will do computations for all the windows. However, I have found it particularly difficult to relate these measures to the window's performance in an easy and intuitive way.

For example, the last one, equivalent noise bandwidth is defined as the ideal rectangular spectral response (the ideal filter) that will pass the same noise power as the window. In other words, this looks like looking for the ideal filter that would pass the same signal power. Equivalent noise bandwidth would usually be expressed as the ratio of the pass band of this ideal filter to the actual pass band. Presumably, the larger the transition band of a filter, the higher the ratio of the pass band of the needed ideal filter to the desired pass band.

But this is just an example. The rest can get more or less complex. Usually, it is said that windows with low (large negative dB) highest sidelobe level and low worst-case processing loss are better.