Hi. I am implementing some FFT software and I'm pondering different ways of averaging FFTs.. Normally most people average the amplitude of each FFT to reduce the variance of the noise. It so happens that in my application we are sampling synchronously with the signal we are interested in (and it's centre-cell) so the phase of the desired signal between each FFT should be the same - this led me to conclude that perhaps more can be gained from averaging the original complex-number FFTs. Presumably the noise suffers from random phase and this will help reduce the noise further, whereas the signal we're interested in has constant (and hence reinforcing) phase. Performing the averaging in this fashoin does indeed show the noise floor falling. Is this be a genuine way to reduce the noise floor further? Even if the signals were not synchronous you might imagine advancing the phase of each FFT bin to ensure the phases line up - so is the reason this method is not always used due to the cost of this phase shifting? Cheers! This message was sent using the Comp.DSP web interface on www.DSPRelated.com
FFT Averaging
Started by ●October 20, 2005
Reply by ●October 20, 20052005-10-20
kyle wrote:> Hi. > > I am implementing some FFT software and I'm pondering different ways of > averaging FFTs.. > > Normally most people average the amplitude of each FFT to reduce the > variance of the noise. > > It so happens that in my application we are sampling synchronously with > the signal we are interested in (and it's centre-cell) so the phase of the > desired signal between each FFT should be the same - this led me to > conclude that perhaps more can be gained from averaging the original > complex-number FFTs. Presumably the noise suffers from random phase and > this will help reduce the noise further, whereas the signal we're > interested in has constant (and hence reinforcing) phase. Performing the > averaging in this fashoin does indeed show the noise floor falling. > > Is this be a genuine way to reduce the noise floor further?This is called coherent averaging. It is legitimate. Radars do this all the time.> > Even if the signals were not synchronous you might imagine advancing the > phase of each FFT bin to ensure the phases line up - so is the reason this > method is not always used due to the cost of this phase shifting? > > Cheers! >In other words if you synchronize the signals then you can use coherent averaging? Certainly true, but if synchronization is lost then results can be disastrous -- you could get perfect cancellation! John
Reply by ●October 21, 20052005-10-21
In rotating machine analysis this technology has been used for more than 30 years and it is widely accepted. It is just called time-synchronize averaging. You can search the Internet with these key words and hundreds of companies will pop up.
Reply by ●October 21, 20052005-10-21
If sequential FFT complex value averages do not depend on previous data segments (used for last FFT average), it would be a lot more efficient to average the data segments and do a single FFT than to FFT each data segment and average the FFT complex values. Windowing, if desired could be done on the average of the data segments, once per FFT. If the data segments are used in more then 1 FFT average (some data overlap), you may still be able to come up with something in a similar manner that is more efficient . Dirk
Reply by ●October 23, 20052005-10-23
You do understand you are doing a portion of a zoom FFT when you add the complex values together. You run the risk that your signal will not be in the exact center of the bin so it may not be seen by the FFT. In article <XoednZD-d4pwG8reRVn-uQ@giganews.com>, "kyle" <kyleblay@blerk.org> wrote:>Hi. > >I am implementing some FFT software and I'm pondering different ways of >averaging FFTs.. > >Normally most people average the amplitude of each FFT to reduce the >variance of the noise. > >It so happens that in my application we are sampling synchronously with >the signal we are interested in (and it's centre-cell) so the phase of the >desired signal between each FFT should be the same - this led me to >conclude that perhaps more can be gained from averaging the original >complex-number FFTs. Presumably the noise suffers from random phase and >this will help reduce the noise further, whereas the signal we're >interested in has constant (and hence reinforcing) phase. Performing the >averaging in this fashoin does indeed show the noise floor falling. > >Is this be a genuine way to reduce the noise floor further? > >Even if the signals were not synchronous you might imagine advancing the >phase of each FFT bin to ensure the phases line up - so is the reason this >method is not always used due to the cost of this phase shifting? > >Cheers! > > > >This message was sent using the Comp.DSP web interface on >www.DSPRelated.com
Reply by ●October 23, 20052005-10-23
>You do understand you are doing a portion of a zoom FFT when you add the >complex values together. You run the risk that your signal will not bein the>exact center of the bin so it may not be seen by the FFT.No I have no idea what you mean... a zoom FFT? I'll search around to find out what you mean but if you have a nice succinct description of the effect you are talking about that would be super :) This message was sent using the Comp.DSP web interface on www.DSPRelated.com
Reply by ●October 24, 20052005-10-24
"kyle" <kyleblay@blerk.org> wrote in news:7emdnSY4qYbHv8HeRVn-uQ@giganews.com:>>You do understand you are doing a portion of a zoom FFT when you add >>the complex values together. You run the risk that your signal will >>not be > in the >>exact center of the bin so it may not be seen by the FFT. > > No I have no idea what you mean... a zoom FFT? I'll search around to > find out what you mean but if you have a nice succinct description of > the effect you are talking about that would be super :) > > > > This message was sent using the Comp.DSP web interface on > www.DSPRelated.com >I zoom FFT is where multiply by a rotating vector so that you can look at a subset of the spectrum. I know that what I just wrote is confusing. Here is an example: Let say that you are sampling at 51.2 KHz and that you are performing a 1024 point FFT. You might create a power spectrum by squaring the real and imaginary components of the FFT. The frequency range would be 0 - 25.6K divided into 512 bins of bandwidth 50 Hz. Now lets say you were really interested in just a small portion of the 0 - 25.6K spectrum. A zoom FFT multiplies the input samples by e^jwt to translate a portion of the signal to DC and then a new FFT is calculated. A 10x zoom might be used create a new spectrum from 1000 - 3560 Hz with a resolution of 5 Hz in each bin. You don't know what happens outside of this region but you can see more detail in the band of interest. It also take 10 times as many samples since BT >= 1. -- Al Clark Danville Signal Processing, Inc. -------------------------------------------------------------------- Purveyors of Fine DSP Hardware and other Cool Stuff Available at http://www.danvillesignal.com