📑 Table of Contents▼

In time series analysis, Bartlett's method (also known as the method of averaged periodograms[1]), is used for estimating power spectra. It provides a way to reduce the variance of the periodogram in exchange for a reduction of resolution, compared to standard periodograms.[2][3] A final estimate of the spectrum at a given frequency is obtained by averaging the estimates from the periodograms (at the same frequency) derived from non-overlapping portions of the original series.

The method is used in physics, engineering, and applied mathematics. Common applications of Bartlett's method are frequency response measurements and general spectrum analysis.

The method is named after M. S. Bartlett who first proposed it.[2][3]

Definition and procedure

edit
The linear spectrum calculated by Bartlett's method.

Bartlett's method consists of the following steps:

  1. The original N point data segment is split up into K (non-overlapping) data segments, each of length M
  2. For each segment, compute the periodogram by computing the discrete Fourier transform (DFT version which does not divide by M), then computing the squared magnitude of the result and dividing this by M.
  3. Average the result of the periodograms above for the K data segments.
    1. The averaging reduces the variance, compared to the original N point data segment.

The result is an array of power measurements vs. frequency "bin".

edit
  • The Welch method: this is a method that uses a modified version of Bartlett's method in which the portions of the series contributing to each periodogram are allowed to overlap.
  • Periodogram smoothing.

References

edit
  1. ^ Engelberg, S. (2008), Digital Signal Processing: An Experimental Approach, Springer, Chap. 7 p. 56
  2. ^ a b Bartlett, M.S. (1948). "Smoothing Periodograms from Time-Series with Continuous Spectra". Nature. 161 (4096): 686–687. Bibcode:1948Natur.161..686B. doi:10.1038/161686a0. S2CID 4068259.
  3. ^ a b Bartlett, M.S. (1950). "Periodogram Analysis and Continuous Spectra". Biometrika. 37 (1–2): 1–16. doi:10.1093/biomet/37.1-2.1. PMID 15420244.

Further reading

edit
Stub icon

This statistics-related article is a stub. You can help Wikipedia by adding missing information.

📚 Artikel Terkait di Wikipedia

Welch's method

frequency domain. Welch's method is an improvement on the standard periodogram spectrum estimating method and on Bartlett's method, in that it reduces noise

Scientific method

The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental

Runge–Kutta methods

Runge–Kutta methods (English: /ˈrʊŋəˈkʊtɑː/ RUUNG-ə-KUUT-tah) are a family of implicit and explicit iterative methods, which include the Euler method, used

Periodogram

not. Time-averaging is also the purview of other articles (Bartlett's method and Welch's method). This article is not about time-averaging. The definition

Spectral density estimation

estimate Welch's method a windowed version of Bartlett's method that uses overlapping segments Multitaper is a periodogram-based method that uses multiple

MUSIC (algorithm)

Spectral density estimation Periodogram Matched filter Welch's method Bartlett's method SAMV (algorithm) Radio direction finding Pitch detection algorithm

M. S. Bartlett

parenting a daughter. Bartlett died in Exmouth, Devon. Bartlett is known for Bartlett's method for estimating power spectra and Bartlett's test for homoscedasticity

Discrete Fourier transform

this context); two examples of such techniques are the Welch method and the Bartlett method; the general subject of estimating the power spectrum of a noisy