Algorithms for Spectral Analysis of Irregularly Sampled Time Series. n this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.
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References in zbMATH (referenced in 5 articles , 1 standard article )
Showing results 1 to 5 of 5.
- Popiński, Waldemar: On least squares discrete Fourier analysis of unequally spaced data (2020)
- Ghaderpour, Ebrahim; Pagiatakis, Spiros D.: Least-squares wavelet analysis of unequally spaced and non-stationary time series and its applications (2017)
- Seilmayer, Martin; Ratajczak, Matthias: A guide on spectral methods applied to discrete data in one dimension (2017)
- Goerg, Georg M.: A nonparametric frequency domain EM algorithm for time series classification with applications to spike sorting and macro-economics (2011)
- Adolf Mathias; Florian Grond; Ramon Guardans; Detlef Seese; Miguel Canela; Hans Diebner: Algorithms for Spectral Analysis of Irregularly Sampled Time Series (2004) not zbMATH