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2 results

  • 18 - Power Spectrum, Cospectrum, and Coherence

  • Chunyan Li, Louisiana State University
  • Book:
    Time Series Data Analysis in Oceanography
    Published online:
    21 April 2022
    Print publication:
    05 May 2022, pp 331-347

  • Summary

    The objective of this chapter is to present some important relations between the Fourier Transform and correlation functions. It turns out that the cross-correlation function and autocorrelation function have some useful relationships to Fourier Transform and power spectrum of the individual functions. As a result, cospectrum and coherence (normalized statistical correlation in frequency domain) can be defined.

  • TWO NEW LOWER BOUNDS FOR THE SPARK OF A MATRIX

  • Part of
  • HAIFENG LIU, JIHUA ZHU, JIGEN PENG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 96 / Issue 3 / December 2017
    Published online by Cambridge University Press:
    08 June 2017, pp. 353-360
    Print publication:
    December 2017
    • Article
      • You have access
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  • The $l_{0}$-minimisation problem has attracted much attention in recent years with the development of compressive sensing. The spark of a matrix is an important measure that can determine whether a given sparse vector is the solution of an $l_{0}$-minimisation problem. However, its calculation involves a combinatorial search over all possible subsets of columns of the matrix, which is an NP-hard problem. We use Weyl’s theorem to give two new lower bounds for the spark of a matrix. One is based on the mutual coherence and the other on the coherence function. Numerical examples are given to show that the new bounds can be significantly better than existing ones.