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2 results

  • 6 - The Power Spectrum

  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book:
    Statistical Methods for Climate Scientists
    Published online:
    03 February 2022
    Print publication:
    24 February 2022, pp 126-155

  • Summary

    This chapter introduces the power spectrum. The power spectrum is the Fourier Transform of the autocovariance function, and the autocovariance function is the (inverse) Fourier Transform of the power spectrum. As such, the power spectrum and autocovariance function offer two complementary but mathematically equivalent descriptions of a stochastic process. The power spectrum quantifies how variance is distributed over frequencies and is useful for identifying periodic behavior in time series. The discrete Fourier transform of a time series can be summarized in a periodogram, which provides a starting point for estimating power spectra. Estimation of the power spectrum can be counterintuitive because the uncertainty in periodogram elements does not decrease with increasing sample size. To reduce uncertainty, periodogram estimates are averaged over a frequency interval called the bandwidth. Trends and discontinuities in time series can lead to similar low-frequency structure despite very different temporal characteristics. Spectral analysis provides a particularly insightful way to understand the behavior of linear filters.

  • Chromatic contrast detection in spatial chromatic noise

  • GIANLUCA MONACI, GLORIA MENEGAZ, SABINE SÜSSTRUNK, KENNETH KNOBLAUCH
  • Journal:
    Visual Neuroscience / Volume 21 / Issue 3 / May 2004
    Published online by Cambridge University Press:
    05 April 2005, pp. 291-294

  • The spectral properties of chromatic-detection mechanisms were investigated using a noise-masking paradigm. Contrast-detection thresholds were measured for a signal with a Gaussian spatial profile, modulated in the equiluminant plane in the presence of spatial chromatic noise. The noise was distributed within a sector in the equiluminant plane, centered on the signal direction. Each stimulus consisted of two adjacent fields, one of which contained the signal, separated horizontally by a gap with the same average chromaticity as the uniform background. Observers were asked to judge on which side of the central fixation point the signal was displayed via a two-alternative, forced-choice (2AFC) paradigm. Contrast thresholds were measured for four color directions and three sector widths at increasing levels of the average energy of the axial component of the noise. Results show that contrast thresholds are unaffected by the width of the noise sector, as previously found for temporally modulated stimuli (D'Zmura & Knoblauch, 1998). The results are consistent with the existence of spectrally broadband linear-detection mechanisms tuned to the signal color direction and support the hypothesis of the existence of higher-order color mechanisms with sensitivities tuned to intermediate directions in color space.