Formulas: annex B E6: asd/ESD/periodogram (global)

MIL-STD-810H, Environmental Engineering Considerations and Laboratory Tests

Last Updated 29 Oct 2026

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Formula 1

The basic definition of the windowed two-sided periodogram for an $N$ point digital sequence $\left\{x_{t}, t=1,2, \ldots, N\right\}$ in continuous frequency form is as follows:

\left\{x_{t}, t=1,2, \ldots, N\right\}

Formula 2

\hat{P}^{(p)}(f)=\frac{\Delta t}{N}\left|\sum_{i=1}^{N} w_{i} x_{i} e^{-i 2 \pi f i \Delta t}\right|^{2} \quad \text { for }- .5 \leq f \leq .5

Formula 3

\varepsilon_{r}\left[\hat{G}_{x x}(f)\right] \approx \frac{1}{\sqrt{B_{e} T}}

Formula 4

\left[\hat{G}_{x x}\left(f_{r}\right)\right]=\frac{B_{r}}{B_{e}} \tan ^{-1}\left(\frac{B_{e}}{B_{r}}\right)-1

Formula 5

B_{r} \approx 2 \zeta f_{r}