ADC performance simulation: How to calculate SINAD from FFT? While working on this problem, I started to have doubts that my initial definition of

$$SINAD = 10 \log_{10} \left( \frac{p_f} {\sum_i{(p_i)} - p_0 - p_f} \right)dB$$

is correct. In this equation, $p_x$ is the power the FFT bin at frequency $x$, $p_f$ is the power of the frequency bin containing the signal frequency $f$ and $p_0$ is the DC component. The sum over $i$ accumulates all frequency components, before removing the DC component $p_0$ and the the signal frequency $p_f$.

More specifically, I am unsure about the $\sum_i(p_i)$ part, which I interpreted from the Wikipedia description


  The ratio of (a) the power of original modulating audio signal, i.e., from a modulated radio frequency carrier to (b) the residual audio power, i.e., noise-plus-distortion powers remaining after the original modulating audio signal is removed. With this definition, it is possible to have a SINAD level less than one.


Comparing with the equation, the "original modulating audio signal" is at frequency $f$, which is accounted for in the $p_f$ term from the FFT. The $p_0$ term I got from the following paper, which says to remove the DC component:

In the "Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR" document, it says


  Signal-to-Noise-and Distortion (SINAD, or S/(N + D) is the ratio of the rms signal amplitude to the mean value of the root-sum-square (rss) of all other spectral components, including harmonics, but excluding dc


Looking at these definitions, I can think of another possible definitions of SINAD, namely

$$SINAD = 10 \log_{10} \left( \frac{p_f} { \sqrt{ \sum_i{(p_i^2)} } - p_0 - p_f} \right)dB$$ 

which uses the RSS (root-sum-square) of the noise and distortion bins of the FFT result. But then, what exactly is meant by "mean value" in that document?
If SINAD can be determined from only expected value and variance then it is possible to determine how SINAD transforms. Variance $\sigma^2$ is preserved whereas expected value $\mu$ grows as $ \sqrt{N} $ where N is the sampling set size. Noise + distorsion is assumed to have variance $\sigma^2$.   

Thus the SINAD value would then be determined to become
$$
{\mathrm {SINAD}}={\frac {P_{{\mathrm {signal}}}+P_{{\mathrm {noise}}}+P_{{\mathrm {distortion}}}}{P_{{\mathrm {noise}}}+P_{{\mathrm {distortion}}}}} = 
{\frac {N |\mu|^2+\sigma^2}{\sigma^2}} = N \cdot SNR + 1
$$

I can explain this in more detail if needed.