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Why is the maximum output (s/N) does not depend on the particular shape of the waveform?

eva2
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    Are you familiar with derivation of the matched filter / maximum SNR criterion? – Marcus Müller Dec 24 '16 at 08:49
  • Given that OP had enough time to specify what exactly they had a problem with, I just voted to close this question as unclear. Eva2, please feel encouraged to specify what exactly in the classical (matrix algebra) max-SNR derivation you don't understand, for example, based on citing the formulas from the wikipedia "matched filter" article. – Marcus Müller Dec 24 '16 at 16:44

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For a signal in additive white noise (AWN) in general, or in additive white Gaussian noise (AWGN) in particular, both the signal output at the sampling instant and the standard deviation of the noise output are proportional to the energy of the signal, and do not depend on the shape of the signal at all. The signal output also peaks at the sampling instant. Consequently, the SNR, which is defined as $$\text{SNR at time } t = \frac{\text{signal output at time }t}{\text{noise standard deviation}}$$ has maximum value at the sampling instant, and this maximum SNR value does not depend on the shape of the signal.

For more than what you probably care to know about matched filters, see this answer of mine.

Community
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Dilip Sarwate
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