Hi Jon, This would be great to have if you are willing to share the draft. I am fairly certain the PFB used in PUPPI is also critically-sampled and so this work would be applicable.
Cheers, Nikhil On Fri, 4 Feb 2022 at 11:54, Jonathan Le Roy Sievers, Prof < [email protected]> wrote: > Thanks for the links, Danny - I look forward to reading the papers! > > This discussion has reminded me that a summer student of mine worked on > inverting critically sampled PFBs. At least for CHIME-type parameters > (1024 channels, 4-bit quantization), he got a method working where you > could essentially perfectly invert them with about a 3% overhead in > bandwidth out of the F-engine. Would that be of general interest? He > started writing up but didn't finish. > > Cheers, > > Jon > ------------------------------ > *From:* Danny Price <[email protected]> > *Sent:* Friday, February 4, 2022 10:02 AM > *To:* [email protected] <[email protected]>; Nikhil > Mahajan <[email protected]>; Jonathan Le Roy Sievers, Prof < > [email protected]> > *Subject:* Re: [casper] Inverting the Polyphase Filter Bank > > > Hi Nikhil, > > > > To add to Cynthia/Jon’s response on the actual inversion, the MWA is > successfully inverting their PFB and have a few publications which detail > it: > > > > https://ui.adsabs.harvard.edu/abs/2020JAI.....950004M/abstract > > https://ui.adsabs.harvard.edu/abs/2020PASA...37...34M/abstract > > > > Good luck on your PUPPI inversion quest! > > > > Cheers, > > Danny > > > > *From: *Hsin Cynthia Chiang, Prof <[email protected]> > *Date: *Friday, 4 February 2022 at 10:34 pm > *To: *[email protected] <[email protected]>, Nikhil > Mahajan <[email protected]>, Jonathan Le Roy Sievers, Prof < > [email protected]> > *Subject: *Re: [casper] Inverting the Polyphase Filter Bank > > Hi Nikhil, > > > > I forwarded your message to Jon Sievers, who I'm cc-ing here, and I'm > passing along a message and attachment from him. > > > > cheers, > > Cynthia > > > > *-------------------------------* > > *From:* Jonathan Le Roy Sievers, Prof <[email protected]> > <[email protected]> > *Sent:* Friday, February 4, 2022 9:02 AM > *To:* [email protected] <[email protected]> > <[email protected]> > *Subject:* Re: [casper] Inverting the Polyphase Filter Bank > > > > Not sure if I'm allowed to post to CASPER since I'm not actually on the > mailing list (but would be glad to be added!). Find attached a note on how > to invert PFBs including Wiener filtering (which you absolutely will want > if you're working with any quantization post-PFB ). Very simple python > code, where window is the window function used in the initial PFB and > thresh roughly the quantization noise vs PFB RMS (so ~0.1 for 4-bit data) > is below. I do have a GPU version in case you're trying to invert huge > quantities of data - my 3070 will invert gigasamples/second with it. > > > > def inverse_pfb_fft_filt(dat,ntap,window=pfb.sinc_hamming,thresh=0.0): > > dd=np.fft.irfft(dat,axis=1) > > win=window(ntap,dd.shape[1]) > > win=np.reshape(win,[ntap,len(win)//ntap]) > > mat=np.zeros(dd.shape,dtype=dd.dtype) > > mat[:ntap,:]=win > > matft=np.fft.rfft(mat,axis=0) > > ddft=np.fft.rfft(dd,axis=0) > > if thresh>0: > > filt=np.abs(matft)**2/(thresh**2+np.abs(matft)**2)*(1+thresh**2) > > ddft=ddft*filt > > return np.fft.irfft(ddft/np.conj(matft),axis=0) > > > > Cheers, > > > > Jon > > > > > > > > On 2022-02-04 00:09, Nikhil Mahajan wrote: > > Dear CASPERites, > > > > I am a graduate student at the University of Toronto (working with Marten > van Kerkwijk) and I have some raw baseband data collected using PUPPI > (Arecibo) - and I am on a quest to invert the polyphase filter bank. I have > 32 channels of complex-baseband that I would very much like to combine into > a single 100 MHz bandwidth stream. > > > > To do this, I would need to understand some of the specifics of the filter > bank pipeline (so that I can successfully invert each step). This is my > current understanding of what happened to the data I have: > > > > 1. Real-valued data sampled at 200 MS/s arrives at the Casper BEE2 board. > > 2. This goes through a real-input PFB implementation such as > `pfb_fir_real` and using a 12-tap, 64-branch polyphase filter (I have the > filter coefficients that were used here). This step outputs 64 streams of > real-valued data. > > 3. Then, for the DFT step of the filterbank, the 64 real-valued streams > are passed through the `fft_wideband_real` block to get 32 channels of > complex-valued data. > > 4. This is then saved to disk. > > > > (I hope someone familiar with PUPPI can correct me here if I am wrong > about any of the above) > > > > Step 3 is the step I am confused about. `fft_wideband_real` does not > appear to be a conventional real-input N-point FFT implementation (Else I > would have N/2 + 1 channels instead of just N/2). Some documentation on > this block says that it "computes the real-sampled Fast Fourier Transform > using the standard Hermitian conjugation trick". What is this standard > Hermitian conjugation trick? I am totally unfamiliar with this. Would I be > wrong in guessing it uses some sort of trick to convert 64 real numbers to > 32 complex numbers and then applies a regular ol' complex-valued FFT on > them? > > > > Thank you so much! I appreciate any and all guidance this mailing list can > provide. > > > > Cheers, > Nikhil Mahajan > > > > -- > You received this message because you are subscribed to the Google Groups > "[email protected]" <[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/CAA39X0%2B3z051d%2B%2BAB0D%3D1LHNHdOSDJp6JEYzzRXatj-ij11_qA%40mail.gmail.com > <https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/CAA39X0%2B3z051d%2B%2BAB0D%3D1LHNHdOSDJp6JEYzzRXatj-ij11_qA%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/e7ea3a41-a9a3-86ff-8008-7724da4c8612%40mcgill.ca > <https://groups.google.com/a/lists.berkeley.edu/d/msgid/casper/e7ea3a41-a9a3-86ff-8008-7724da4c8612%40mcgill.ca?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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