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  1. How can we determine whether the receive filter is optimal or not in a digital receiver?
  2. For a decision region, how can we choose a noise value zk?
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closed as unclear what you're asking by Dilip Sarwate, jonsca, penelope, nispio, Peter K. Nov 17 '13 at 18:55

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ There is so much information missing from this question that it's hard to know where to start. Please fill in details and let's see if we can re-open and answer it. $\endgroup$ – Peter K. Nov 17 '13 at 18:55
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  1. It depends upon the modulation scheme that is being used. You calculate the probability of a bit error using your receiver of choice, then based on the characteristics of the systems in use, you calculate or bound the best probability of error that you could possibly get, then compare the two answers. For linear modulation on the additive-white-Gaussian-noise (AWGN) channel, the optimum receiver filter is one whose impulse response is matched to the pulse shape used at the transmitter.

  2. It's not clear what you're asking. Noise values aren't typically something that you choose; nature does.

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