Correlation between amplitude and power

In this link on page 218, just before the first paragraph ends, it says: " We can interpret the power axes as one-half the square [...] of the modulus of the complex envelope."

In the same paragraph, the average input power is stated to be $P_\text{in} = A^2/2$. Can somebody please explain to me, why there is no resistance ? The amplitude probably refers to a voltage signal. The RMS of a sinusoidal signal is $A/\sqrt(2)$. Since this is the square root of the mean, it makes sense to me, that the average input poewr is $A^2/2$. But still, I am confused about the lacking resistance. Especially, since in the second paragraph, it is stated, that the power axis will be graduated in units of $10\log(P_\text{in})$.

• Often, there is some statement somewhere, according to "Amplitudes are normalized to a 1Ohm load" or something similar. Normalizations are very common in DSP, otherwise, we would also need to take care of the unit of impulse responses, time and so on. – Maximilian Matthé Feb 15 '17 at 6:34