Hi Colm, Just to add -- you might find this ipython notebook a useful place to start poking around if you want to do some software sims -- https://github.com/telegraphic/pfb_introduction/blob/master/pfb_introduction.ipynb
On Fri, 28 Aug 2020 at 17:17, Ross Martin <[email protected]> wrote: > Hi Colm, > > I realized that I forgot to mention that time resolution and response > duration aren't exactly the same thing. > > When you switch from an FFT to a PFB with an equivalent number of > channels, the PFB filter has a length equal to N FFTs. So your time > response length becomes longer by a factor of N. However, the PFB output > still has a definite and distinct peak that hasn't really changed in width > from the original FFT case. > > So for many ways of measuring time resolution, switching from FFT to PFB > doesn't change time resolution much, even though it does extend the time > length of the response. > > Regards, > > Ross > > [email protected] > > > On Fri, Aug 28, 2020, 7:58 AM Ross Martin <[email protected]> wrote: > >> Hi Colm, >> >> Events with narrow time resolution will have larger bandwidth, which >> means that energy from them will appear in multiple PFB output channels. >> >> If you retain only a single PFB output channel, then you have lost time >> resolution exactly as described by previous answers. >> >> However, PFBs, when done correctly, are invertible. If you retain *all* >> PFB channels, you can reconstruct the entire original time series (with >> some controllable processing noise). Since you can reconstruct all your >> original data, you've lost nothing at all regarding time resolution (or >> anything else). Fine time resolution can be hard to see in this form, but >> all the data is there to extract it. >> >> It's also possible to invert part of a PFB. For example, if an event has >> energy primarily in three adjacent channels, you can keep just those three >> channels and invert just the three channels. This effectively gives you a >> bandpass filter with three times the channel bandwidth, and three times >> finer time resolution than the time resolution of a single channel. >> >> Regarding your second question of whether amplitude of an off-center sine >> wave varies. It essentially does not. A PFB, when properly constructed, >> is exactly equivalent to a complex mixer, followed by a lowpass filter, >> followed by a downsampler. (Presentation on my web site.). For an >> off-center sine wave these steps will give as a primary output signal a >> complex sine wave whose amplitude is constant but phase varies. There will >> also be secondary aliased output components, that do distort the amplitude >> measurement a little. However, these components will certainly be in the >> stopband of the filter, and with even weak PFB filters be at least 60dB >> down. If that's too much amplitude measurement variation, you can get >> stronger PFB filters -- but these will give you lower time resolution in a >> single output channel. >> >> Regards, >> >> Ross >> >> [email protected] >> >> >> >> >> On Fri, Aug 28, 2020, 3:40 AM Colm Bracken <[email protected]> wrote: >> >>> Hi James, >>> >>> Perfect, thanks so much. >>> It is good to have clarity on these matters. >>> >>> Best wishes, >>> Colm >>> >>> On Fri, 28 Aug 2020 at 12:23, James Smith <[email protected]> wrote: >>> >>>> Hello Colm, >>>> >>>> Yes, you're correct. That's how some of our narrowband designs work - >>>> you use each PFB channel as a very narrow bandpass filter, and treat its >>>> output as a complex time-series. So you can pass it through another PFB to >>>> get a higher-resolution spectrum, at the expense of very much lower time >>>> resolution of course. >>>> >>>> Regards, >>>> James >>>> >>>> >>>> On Fri, Aug 28, 2020 at 11:04 AM Colm Bracken <[email protected]> >>>> wrote: >>>> >>>>> Hi Cedric, >>>>> >>>>> Great, thanks for confirming that. >>>>> One more question, if you don't mind? >>>>> >>>>> If a narrow band signal is off-centre relative to one of my frequency >>>>> bins, will the measured amplitude change each time I run the FFT? >>>>> For example, if my FFT frequency bins are exactly 1 MHz wide (1024 pt >>>>> FFT applied to 1 GSPS ADC data), and I am trying to measure a sinusoid >>>>> with >>>>> a frequency of 5.1 MHz, will the measured amplitude oscillate at a >>>>> frequency of 0.1 MHz (5.1 MHz - 5 MHz)? Basically, my sampling (in terms >>>>> of >>>>> how often I sample the full time stream for the FFT) is out of phase with >>>>> the signal to be measured? >>>>> >>>>> I probably didn't explain that very well, apologies. >>>>> >>>>> Best wishes, >>>>> Colm >>>>> >>>>> On Fri, 28 Aug 2020 at 11:17, 'Cedric Viou' via >>>>> [email protected] <[email protected]> wrote: >>>>> >>>>>> Hi Colm, >>>>>> >>>>>> You are right. >>>>>> >>>>>> PFB is a great way to reduce frequency smearing but the down-side is >>>>>> time smearing. >>>>>> >>>>>> A brief event will be convolved with at least one of your PFB 8-tap >>>>>> filters that end up feeding several FFT computations in a row. >>>>>> So, you get time smearing for that short event... >>>>>> >>>>>> Regards, >>>>>> >>>>>> Cedric >>>>>> >>>>>> >>>>>> Le 28/08/2020 à 11:56, Colm Bracken a écrit : >>>>>> > Hi All, >>>>>> > >>>>>> > I have a question, which is probably DSP 101 basics, but I just >>>>>> wasn't 100% sure. >>>>>> > >>>>>> > If I am applying a 1024 point FFT to a continuous time-stream from >>>>>> an ADC with sampling ~ 1 GSPS, I will have a time resolution ~ 1 >>>>>> microsecond (and frequency res. of ~ 1 MHz). >>>>>> > >>>>>> > But, if I instead apply an 8 tap PFB, am I essentially smearing out >>>>>> my time resolution by a factor of 8, since I am now summing 8 rows of my >>>>>> 1024 point time streams? >>>>>> > I can't see how the number of PFB taps wouldn't affect my time >>>>>> resolution. Or am I missing something? >>>>>> > >>>>>> > Thanks in advance, >>>>>> > Colm >>>>>> > >>>>>> > -- >>>>>> > >>>>>> > *Dr Colm Bracken* >>>>>> > Lecturer >>>>>> > Maynooth University Experimental Physics >>>>>> > >>>>>> > >>>>>> > Maynooth University, Maynooth, Co. Kildare, Ireland. >>>>>> > >>>>>> > T: +353 1 708 3641 >>>>>> > E: [email protected] <mailto:[email protected]> W: >>>>>> www.maynoothuniversity.ie <http://www.maynoothuniversity.ie> >>>>>> > >>>>>> > Follow my work on https://nuim.academia.edu/ColmBracken >>>>>> > >>>>>> > >>>>>> > >>>>>> > And >>>>>> > >>>>>> > >>>>>> > Research Associate >>>>>> > >>>>>> > Astronomy & Astrophysics Section >>>>>> > School of Cosmic Physics >>>>>> > Dublin Institute for Advanced Studies >>>>>> > 31 Fitzwilliam Place >>>>>> > Dublin 2, D02 XF86 >>>>>> > >>>>>> > >>>>>> > >>>>>> > T: +353 1 440 6656 ext 352 >>>>>> > E: [email protected] <mailto:[email protected]> W: >>>>>> www.dias.ie/2017/06/22/dr-colm-bracken < >>>>>> https://www.dias.ie/2017/06/22/dr-colm-bracken> >>>>>> > >>>>>> > Follow my work on https://nuim.academia.edu/ColmBracken >>>>>> > >>>>>> > -- >>>>>> > You received this message because you are subscribed to the Google >>>>>> Groups "[email protected]" group. >>>>>> > To unsubscribe from this group and stop receiving emails from it, >>>>>> send an email to [email protected] <mailto: >>>>>> [email protected]>. >>>>>> > To view this discussion on the web visit >>>>>> https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/CAEx9wh9GmrYZ7_uLkXwSKqOp3GYm1Ei_0Bq-TPg9pt8LgQdprw%40mail.gmail.com >>>>>> < >>>>>> https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/CAEx9wh9GmrYZ7_uLkXwSKqOp3GYm1Ei_0Bq-TPg9pt8LgQdprw%40mail.gmail.com?utm_medium=email&utm_source=footer >>>>>> >. >>>>>> >>>>>> -- >>>>>> Cedric Viou <[email protected]> >>>>>> >>>>>> Ingénieur de recherche >>>>>> >>>>>> Station de Radioastronomie de Nançay, >>>>>> Observatoire de Paris, PSL Research University, CNRS, Univ. Orléans, >>>>>> OSUC, >>>>>> 18330 Nançay, France >>>>>> http://www.obs-nancay.fr/ >>>>>> >>>>>> phone : +33 (0) 248 51 8609 >>>>>> fax : +33 (0) 248 51 8318 >>>>>> >>>>>> www.openstreetmap.org/?mlat=47.381848&mlon=2.194415&zoom=18 >>>>>> >>>>>> -- >>>>>> You received this message because you are subscribed to the Google >>>>>> Groups "[email protected]" group. >>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>> send an email to [email protected]. >>>>>> To view this discussion on the web visit >>>>>> https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/68a23cbf-5320-8b50-7a4f-52379c4a2ad7%40obs-nancay.fr >>>>>> . >>>>>> >>>>> >>>>> >>>>> -- >>>>> >>>>> *Dr Colm Bracken* >>>>> Lecturer >>>>> Maynooth University Experimental Physics >>>>> >>>>> >>>>> Maynooth University, Maynooth, Co. Kildare, Ireland. >>>>> >>>>> T: +353 1 708 3641 >>>>> E: [email protected] W: www.maynoothuniversity.ie >>>>> >>>>> Follow my work on https://nuim.academia.edu/ColmBracken >>>>> >>>>> >>>>> >>>>> And >>>>> >>>>> >>>>> Research Associate >>>>> >>>>> Astronomy & Astrophysics Section >>>>> School of Cosmic Physics >>>>> Dublin Institute for Advanced Studies >>>>> 31 Fitzwilliam Place >>>>> Dublin 2, D02 XF86 >>>>> >>>>> >>>>> >>>>> T: +353 1 440 6656 ext 352 >>>>> E: [email protected] W: www.dias.ie/2017/06/22/dr-colm-bracken >>>>> >>>>> Follow my work on https://nuim.academia.edu/ColmBracken >>>>> >>>>> -- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "[email protected]" group. >>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>> an email to [email protected]. >>>>> To view this discussion on the web visit >>>>> https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/CAEx9wh_2SWV5ahQ7x4bCegn9WkZ%3DPket18wO0QnLb%2BZx8JD7Lw%40mail.gmail.com >>>>> <https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/CAEx9wh_2SWV5ahQ7x4bCegn9WkZ%3DPket18wO0QnLb%2BZx8JD7Lw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>> . >>>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "[email protected]" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To view this discussion on the web visit >>>> https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/CAG67D37EFydE4i2WtHH43SC8oGS_Cwv4VCAHCXhp4SNMEOqzXg%40mail.gmail.com >>>> <https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/CAG67D37EFydE4i2WtHH43SC8oGS_Cwv4VCAHCXhp4SNMEOqzXg%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>> >>> >>> -- >>> >>> *Dr Colm Bracken* >>> Lecturer >>> Maynooth University Experimental Physics >>> >>> >>> Maynooth University, Maynooth, Co. 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