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The gaussian function, an exponential function with a negative square of the argument in the exponent, is interesting in signal processing because the Fourier Transform of a gaussian function is also a gaussian function.

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How do I add AWGN to an I and Q representation of a signal?

Yes, you can add AWGN of variance $\sigma^2$ separately to each of the two terms, because the sum of two Gaussians is also a Gaussian and their variances add up. …
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