minimum requirement of SNR for fft algorithm
Some assumptions are made in this paragraph. The signal is sinusoidal. It lands exactly at a frequency domain bin, and has magnitude $a$. No frequency domain interpolation is needed. Frequency estimation will look for and report the bin with the largest magnitude. This can be the signal bin or a noise-only bin. The noise is additive, but its contribution to the signal bin will be ignored as an approximation. The real $\operatorname{Re}(Z)$ and imaginary $\operatorname{Im}(Z)$ components of the noise $Z$ in the noise-only bins are independent and identically distributed (IID) Gaussian random variables of zero expected value.

The probability that the magnitude of the noise, at a given noise-only bin, is lower than $a$ is given by the cumulative distribution function of the Rayleigh distribution:

$$P(|Z| &lt; a) = 1-\operatorname{exp}\left(\frac{-a^{2}}{2\sigma^2}\right),$$

where $\sigma^2 = E\left(\operatorname{Re}(Z)^2\right) = E\left(\operatorname{Im}(Z)^2\right)$, the expected value of both the squared real and imaginary components of $Z$. If there are $N$ bins to look in, then the probability that none of the noise-only bins has higher magnitude than the signal bin is given by:

$$P(|Z| &lt; a)^{N-1}.$$

A conclusion is that the correct bin will be chosen at a higher probability if you can narrow down the frequency range where to look for the signal, making $N$ smaller. It is up to you/someone to decide how much risk of reporting the wrong bin is acceptable. There is more to say about this I'm sure.