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:

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?

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Could you elaborate more on how you've come up with the sum over $i$ and what $p_f$ and $p_0$ are? –  Phonon Feb 15 '13 at 18:31
@Phonon, I tried to clarify. Let me know if it needs some more. Thanks. –  FriendFX Feb 17 '13 at 23:05