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

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