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. 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_tQLMpLNvcCkjSW-M_KNiAC96R-g-oGShBQKzj65F_RQ%40mail.gmail.com >> <https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/CAEx9wh_tQLMpLNvcCkjSW-M_KNiAC96R-g-oGShBQKzj65F_RQ%40mail.gmail.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "[email protected]" group. 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