Hello experts, I was cruising on Internet for faily long time and I could not get the answer to my questions regarding windowgin procedure. 1. Everybody are writing how good windowing is for supressing leakage (amplitudes at frequencies higher and lower than the signal frequency). However nobody says how much it supresses amplitude at signal frequency itself. It surely must suppress it a bit, after all if you multiply signal with something LESS than 1 it must be smaller. But how much? (if possible, make an estimate at least for Hann window) 2. Windowing is designed for getting rid of edge effects, that is, voltage is changing between -1 and 1 V, you can start with signal of -1 V and end with signal + 0.5 V, hence edge. However, I have a different problem, my signal is positioned ON carrier, which changes without any order between say -10 V and 10 V. So what happens is that I can start with - 5V and end with + 7 V, despite my signal is only 1 V large. Is windowing good for this situation too? Or should I try something else? Thanks for the answer, Marko.

# How much do Windowing procedures harm the signal?

Started by ●December 23, 2006

Reply by ●December 23, 20062006-12-23

Pygmalion skrev:> Hello experts, > > I was cruising on Internet for faily long time and I could not get the > answer to my questions regarding windowgin procedure. > > 1. Everybody are writing how good windowing is for supressing leakage > (amplitudes at frequencies higher and lower than the signal frequency). > However nobody says how much it supresses amplitude at signal > frequency itself. It surely must suppress it a bit, after all if you > multiply signal with something LESS than 1 it must be smaller. But how > much? (if possible, make an estimate at least for Hann window)The question can not be answered. Multiplication in time domain corresponds to convolution in frequency domain. So each frequency component in the "true" periodogram is modified according to the sidelobes of the window function and the rest of the "true" periodogram. Do note that the truncated data set corresponds to convolving the "true" periodogram of a random process of infinite duration with the spectrum of the rectangular window function. This repesents a certain amount of spectral leakage. Window functions are used because they trade some of this spectrum leakage for a smoother spectrum.> 2. Windowing is designed for getting rid of edge effects, that is, > voltage is changing between -1 and 1 V, you can start with signal of -1 > V and end with signal + 0.5 V, hence edge.Wrong. Windowing is used to reduce sidelobes in the spectrum. Rune

Reply by ●December 23, 20062006-12-23

There is a definitive paper written on this very subject - "On Use of Windows for Harmonic Analysis with the Discrete Fourier Transform," by Frederick Harris, Proceedings of the IEEE Vol 66 No.1 (c. 1978). He discusses and tabulates many facets of over 20 window functions, including the one you mention. Jeff

Reply by ●December 23, 20062006-12-23

Pygmalion wrote:> Hello experts, > > I was cruising on Internet for faily long time and I could not get the > answer to my questions regarding windowgin procedure. > > 1. Everybody are writing how good windowing is for supressing leakage > (amplitudes at frequencies higher and lower than the signal frequency). > However nobody says how much it supresses amplitude at signal > frequency itself. It surely must suppress it a bit, after all if you > multiply signal with something LESS than 1 it must be smaller. But how > much? (if possible, make an estimate at least for Hann window)It's only the relative amplitudes of the signal and the leakage that matters. If the signal is reduces to half it's unwindowsd magnitude and leakage is reduced to 1 tenth. multiplying by 2 makes that unchanged and one fifth.> 2. Windowing is designed for getting rid of edge effects, that is, > voltage is changing between -1 and 1 V, you can start with signal of -1 > V and end with signal + 0.5 V, hence edge. However, I have a different > problem, my signal is positioned ON carrier, which changes without any > order between say -10 V and 10 V. So what happens is that I can start > with - 5V and end with + 7 V, despite my signal is only 1 V large. Is > windowing good for this situation too? Or should I try something else?Bringing both ends of your sequence smoothly to zero eliminates the effect you describe. That's why windowing works. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●December 24, 20062006-12-24

"Rune Allnor" <allnor@tele.ntnu.no> wrote in message news:1166911549.729406.18550@i12g2000cwa.googlegroups.com...> >> 2. Windowing is designed for getting rid of edge effects, that is, >> voltage is changing between -1 and 1 V, you can start with signal of -1 >> V and end with signal + 0.5 V, hence edge. > > Wrong. Windowing is used to reduce sidelobes in the spectrum.Hmmm... I should think that the edges are what cause the sidelobes. Witness the FT of a rectangular window and compare it to a triangular window or a raised cosine. Attenuating the edges cause the sidelobes to go down - in general at least - and generally at the expense of the main lobe width. To the OP's question about how much the signal is changed. The window applies to all the signal components equally. The corresponding correlation in frequency that matches the multiplication in time should help make that more evident. Fred

Reply by ●December 24, 20062006-12-24

Pygmalion Harris' paper is one of the best explainations of how and why to window. Be careful of some of the table entries for Blackman and 4-term minimum sidelobe windows. Google on Nuttall and windows to look for references to Albert Nuttall's 1980 paper in the Transactions on ASSP with some corrections. Look for the original paper here: http://www.eng.vt.edu/me5714/textbook/windows.pdf Rune The 'sidelobes' are visible because of signals with discontinuity at the data ends which the FFT treats as circularly connected. Sine or cosine components that are continuous when wrapped have the zeros of their sidelobe patterns at frequency samples so the appearance of the sidelobes is reduced, but I expect you know that ,so Pygmalion's statement was correct. Dale B. Dalrymple http://dbdimages.com

Reply by ●December 24, 20062006-12-24

Jerry Avins wrote:> > 1. Everybody are writing how good windowing is for supressing leakage > > (amplitudes at frequencies higher and lower than the signal frequency). > > However nobody says how much it supresses amplitude at signal > > frequency itself. It surely must suppress it a bit, after all if you > > multiply signal with something LESS than 1 it must be smaller. But how > > much? (if possible, make an estimate at least for Hann window) > > It's only the relative amplitudes of the signal and the leakage that > matters. If the signal is reduces to half it's unwindowsd magnitude and > leakage is reduced to 1 tenth. multiplying by 2 makes that unchanged and > one fifth. >Right. But how do you know how much is the signal's magnitude reduced? And what is the factor to multiply the obtained spectrum to obtain signal's exact amplitude? I really wish to obtain exact amplitude and not so much to get rid of sidelobes. Marko

Reply by ●December 24, 20062006-12-24

> >Jerry Avins wrote: >> > 1. Everybody are writing how good windowing is for supressingleakage>> > (amplitudes at frequencies higher and lower than the signalfrequency).>> > However nobody says how much it supresses amplitude at signal >> > frequency itself. It surely must suppress it a bit, after all ifyou>> > multiply signal with something LESS than 1 it must be smaller. Buthow>> > much? (if possible, make an estimate at least for Hann window) >> >> It's only the relative amplitudes of the signal and the leakage that >> matters. If the signal is reduces to half it's unwindowsd magnitudeand>> leakage is reduced to 1 tenth. multiplying by 2 makes that unchangedand>> one fifth. >> >Right. But how do you know how much is the signal's magnitude reduced? > And what is the factor to multiply the obtained spectrum to obtain >signal's exact amplitude? I really wish to obtain exact amplitude and >not so much to get rid of sidelobes.In the table in Harris's paper, look at the column entitled 'Coherent Gain'. I'm glad someone provided a link to this paper - I have used it for many years as a source of reference, but it was at work, so I couldn't remember exactly where to find the figure you wanted when I made my earlier post. Jeff> >Marko > >

Reply by ●December 24, 20062006-12-24

OK, so it is a usual practice to use windowing, and then divide it with coherent gain in order to obtain real magnitude for oscillation? Regards, Marko Jeff Caunter wrote:> > > >Jerry Avins wrote: > >> > 1. Everybody are writing how good windowing is for supressing > leakage > >> > (amplitudes at frequencies higher and lower than the signal > frequency). > >> > However nobody says how much it supresses amplitude at signal > >> > frequency itself. It surely must suppress it a bit, after all if > you > >> > multiply signal with something LESS than 1 it must be smaller. But > how > >> > much? (if possible, make an estimate at least for Hann window) > >> > >> It's only the relative amplitudes of the signal and the leakage that > >> matters. If the signal is reduces to half it's unwindowsd magnitude > and > >> leakage is reduced to 1 tenth. multiplying by 2 makes that unchanged > and > >> one fifth. > >> > >Right. But how do you know how much is the signal's magnitude reduced? > > And what is the factor to multiply the obtained spectrum to obtain > >signal's exact amplitude? I really wish to obtain exact amplitude and > >not so much to get rid of sidelobes. > > In the table in Harris's paper, look at the column entitled 'Coherent > Gain'. > > I'm glad someone provided a link to this paper - I have used it for many > years as a source of reference, but it was at work, so I couldn't remember > exactly where to find the figure you wanted when I made my earlier post. > > Jeff > > > >Marko > > > >

Reply by ●December 24, 20062006-12-24

> >OK, so it is a usual practice to use windowing, and then divide it with >coherent gain in order to obtain real magnitude for oscillation? >Yes, I would say so. Sometimes, however, this 'comes out in the wash' if you are applying other processes too, and employ some kind of overall calibration factor. Jeff