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I read that the noise reduction of a moving average FIR can be expressed as the square root of N where N is the length of the filter. How do you prove? I can't quite get it.

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Since this is homework/a learning assignment, I think a hint is worth more than the (admittedly done on this site a couple of times) complete proof:

You forgot to also read the context: That's not true for just any noise and any signal, it's only true for noise that's white and a signal that fits perfectly into the filter shape.

Think about what "white" has to do with a moving average. Hope this helps.

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