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For a project I'm trying to implement a BPSK demodulator on some random wave files, I'm getting a few difficulties:

  1. How do I know my bit rate, i.e. how many bits each 'real data bit' I'm having.
  2. How can I figure out the size of my real data.
  3. I don't know exactly the corner frequency $f_c$, is it OK for me to estimate it for the carrier wave?
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  • $\begingroup$ I suggest getting the book "Software Receiver Design" by Johnson, Sethares and Klein. It has the answers you need. $\endgroup$ – MBaz Jun 14 '18 at 13:13
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How do I know my bit rate, i.e. how many bits each 'real data bit' I'm having.

I'm not sure I understand what you're saying, but this is one level "above" BPSK demodulation. What BPSK demodulation gives you are bits. full stop – how you interpret these bits, and whether they have channel coding can't be said without very much additional knowledge about the data.

How can I figure out the size of my real data.

see above.

don't know exactly the corner frequency $f_c$, is it OK for me to estimate it for the carrier wave?

Don't know what that means. You'll need some way to estimate the symbol clock. For BPSK, the typical easy-to-teach approach is squaring timing recovery, where you just "collapse" the modulation by squaring the signal, and then look for autocorrelation peaks.

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