Hey Nikhail, The FFT is a Hermitian function, which means that it has the property:
[image: Screenshot from 2022-02-04 08-34-24.png] This principle is used in the real wideband FFT to compute 2 real FFTs using one complex FFT core - this <http://www.hyperdynelabs.com/dspdude/papers/COMPUTING%20THE%20FFT%20OF%20TWO%20REAL%20SIGNALS%20USING%20A%20SINGLE%20FFT.pdf> paper explains it well. For a detailed explanation on how the CASPER FFT works specifically, Ryan Monroe's paper on Improving the Performance and Resource Utilization of the CASPER FFT and Polyphase FIlterbank goes into quite a lot of detail. You only get 32 output channels because the CASPER wideband FFT discards all negative frequency components as they're just a mirror of positive frequency components and aren't needed. Morag On Fri, Feb 4, 2022 at 7:10 AM Nikhil Mahajan <[email protected]> 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]" 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/CAGH-0Tc%2BWk1JExurEHYFPM8MarkmTY_TnjFqPpjy2a%3D7zqxvng%40mail.gmail.com.
