I want to calculate the SNR for a speech signal recorded within a noisy environment. I also sampled purely the noise within the environment.
The SNR is based on the ratio of power of clean signal and the power of noise signal. So my naive attempt to get SNR is:
$\frac{P_{signal+noise}}{P_{noise}} = \frac{P_{signal} + P_{noise}}{P_{noise}} = \frac{P_{signal}}{P_{noise}} + \frac{P_{noise}}{P_{noise}}= SNR + 1$
$SNR = \frac{P_{signal + noise}}{P_{noise}} - 1$
However I realized that: $P_{signal+noise} \propto (A_{signal} + A_{noise})^2 = A_{signal}^2 + A_{noise}^2 + A_{signal}A_{noise}$ $P_{signal+noise} = P_{signal} + P_{noise} + avg(A_{signal}A_{noise}) \neq P_{signal} + P_{noise}$
I couldn't find anything about this in the Wikipedia article nor other threads with this particular question.