Statistiques et probabilités
Calculatrice vérifiée avec une formule transparente
Allan Variance Calculator.
Estimates the Allan variance and deviation of a dataset from a single sample of phase or frequency measurements, given the sample size and measurement interval.
Vos entrées
Comment ça marche
- 1
Enter the number of samples, averaging time, and phase noise.
- 2
The calculator computes the Allan variance as phase noise squared divided by tau squared times (sample size minus one).
- 3
The Allan deviation is the square root of the variance.
- 4
Review the results and adjust inputs as needed.
(phase_noise^2) / (tau^2 * max(sample_size - 1, 1))Questions fréquentes
What does Allan variance measure?
It quantifies frequency stability as a function of averaging time, helping identify noise types in clocks and oscillators.
Why use sample size minus one?
This approximates the degrees of freedom in the variance estimate, similar to sample variance.
Can I use this for any dataset?
This simplified version assumes white phase noise; for other noise types, more complex estimators are needed.
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Résultats
Formule vérifiéeEstimation à titre indicatif uniquement — vérifiez les décisions importantes avec un professionnel approprié.
Comment ça marche
Estimates the Allan variance and deviation of a dataset from a single sample of phase or frequency measurements, given the sample size and measurement interval.
- Enter the number of samples, averaging time, and phase noise.
- The calculator computes the Allan variance as phase noise squared divided by tau squared times (sample size minus one).
- The Allan deviation is the square root of the variance.
- Review the results and adjust inputs as needed.
Formules
Les mathématiques derrière cette calculatrice, écrites pour que vous puissiez vérifier le résultat.
Allan Variance (simplified)
Estimates variance from phase noise σ_φ, averaging time τ, and sample count N.
Cas d'utilisation réels
Où ce calcul apparaît dans la vie quotidienne.
Oscillator stability
Compare short-term and long-term frequency stability of quartz or atomic clocks.
Example: Evaluate a 10 MHz oscillator with τ from 1 ms to 100 s.
Sensor noise characterization
Assess gyroscope or accelerometer noise for inertial navigation systems.
Example: Determine optimal averaging time for a MEMS gyro.
Conseils et erreurs courantes
Tips
- Use a larger sample size for more reliable estimates.
- Choose tau values spanning decades to see noise type transitions.
- Ensure phase noise is in radians, not degrees.
Common Mistakes to Avoid
- Using sample size instead of sample size minus one.
- Forgetting to square the phase noise.
- Mixing units (e.g., degrees instead of radians).
Hypothèses et limites
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.