# Determining Power of White Noise Component of an Incomplete Time Signal

I want to determine the power of the noise component of a time dependend signal x(t) (similar to picture below)

With constant sampling rate I use Parceval's Therorem and calculate the standard deviation with

$$\sigma^2 = \frac{\text{abs}(\text{FFT}(x))^2}{N}$$

where N is number of data points and fft matlab dft implementation. For the standard deviation according to white noise I remove the discrete frequencies of the spectrum and use above formula with the mean value of the remaining spectrum.

In some signals there are quite a few NaN data points (~ 10%), so said method can not be applied anymore.

Is there a mathematically correct method to determine the power of the noise component of the signal? Interpolation does not seem to be a good solution, because this would lead to an underestimation of the noise.

• The method that you described sounds reasonable already. I don't think you'll find any "mathematically correct" way to handle signals that contain NaNs, as those aren't really a mathematical construct. – Jason R May 22 '14 at 16:35
• There are other ways - for example remove the sinusoid with a narrow notch filter. But you probably need to resolve the NaN issue before any of them will work. – John May 22 '14 at 16:57