Thread View: sci.geo.fluids
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Started by Arthur Mariano
Thu, 08 Oct 1992 15:26
Re: Spectrum of gappy data
Author: Arthur Mariano
Date: Thu, 08 Oct 1992 15:26
Date: Thu, 08 Oct 1992 15:26
35 lines
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2143 bytes
In article <1at2faINN9he@network.ucsd.edu>jasmith@ucsd.edu (jerry smith) writes : > ..... >Covariance-based methods are often referred to as "auto-regressive" models >(or AR-spectra; I can't say why this name has stuck). Marple reviews the >relative advantages of AR versus "periodogram" (fft) and a few others >(e.g. Proni's method). > ..... I would not use AR methods on many oceanographic data sets. AR methods work well for relatively high resolution detection of close peaks. For instance, identifying both a tidal and an inertial peak in data collected at mid-latitudes. An AR(1) filter or Markov model can either act as a high or low pass filter, while an AR(2m) model is used for detecting m sinusoids. Many oceanographic data sets are red and have significant energy in a broad mesoscale range. AR methods which use the sample covariance/autocorrelation were not formulated for this type of spectra. They work well in speech applications and for detecting sinusoids in white noise. To quote from Thomson (1990), "If your spectrum estimate explicitly requires sample autocorrelations you are almost certaintly doing something wrong." My suggestion is to read this paper and his earlier work before you do anything. cheers, arthur Thomas, D.J., 1990: Quadratic-inverse spectrum estimates: applications to palaeoclimatology, Phil. Trans. R. Soc. Lond., 332, 539-597. -- *****************R.I.P., Bill of Rights, 1791-1991******************** Arthur J. Mariano INET: mariano@sgrmag.rsmas.miami.edu Dept. of Meteorology and Physical Oceanography 305-361-4193 Rosenstiel School of Marine and Atmospheric Science, U. of Miami 4600 Rickenbacker Causeway, Miami, FL 33149-1098, USA
Re: Spectrum of gappy data
Author: jerry smith
Date: Thu, 08 Oct 1992 16:26
Date: Thu, 08 Oct 1992 16:26
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In article <1992Oct8.152654.17216@news.miami.edu> Arthur Mariano, mariano@sgrmag.rsmas.miami.edu writes: >An AR(1) filter or Markov model can either >act as a high or low pass filter, while an AR(2m) model is used for >detecting m sinusoids. Many oceanographic data sets are red and have >significant energy in a broad mesoscale range. AR methods which use I don't know why there is so much confusion about this. The same is true of the FFT. The FFT of the covariances is identical to the squared FFT of the time series, in the case of regularly spaced data. This is a mathematical identity. However, when there are many gaps in the data, it is still usually possible to form a "complete" set of covariances to transform into a power spectrum. (The number of degrees of freedom in each estimate of the covariance varies according to the gaps, etc., so there may be some subtleties in assigning confidence limits.) For either approach, squaring the FFT of the timeseries or FFTing the covariances, it is probably wise to separate the mean and trend from the data first. Cheers, -jerry
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