A maximum likelihood estimator for spectral models of acoustic noise processes

• Published in: The Journal of the Acoustical Society of America 2018-03, Vol.143 (3), p.1759-1759
• Main Authors: Lyons, Gregory W., Hart, Carl R.
• Format: Article
• Language: English
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.5035762

The power spectral density of time series from many acoustic phenomena can vary rapidly through several decades of magnitude, particularly for noise processes. This property can complicate evaluation of spectral density models with respect to a non-parametric estimate of the spectral density, also known as the periodogram. Typical measures, such as the sum of squares of the residuals, can suffer from bias errors and oversensitivity to large values. A log-likelihood function is here presented for a periodogram derived from a sequence of independent, circularly-symmetric complex normal Fourier components. The bias-corrected Akaike’s information criterion of an expected-value spectral model is shown to be a useful measure for multi-model selection. A maximum-likelihood estimator is formed for spectral model parameters with respect to a known periodogram, along with approximate confidence intervals for the parameter estimates. Results from the maximum-likelihood estimator are compared with weighted and unweighted least-squares methods by estimating model parameters for periodograms from both synthetic and measured noise time series. Practical considerations for general periodogram fitting and numerical methods are discussed.