Wavelets and LRD (1)

• Let X(t) be LRD process (wide-sense stationary)

  • dj,k: its wavelet coefficients
  • G(n): power spectral density of X(t)
  • Yj(n): spectrum of the wavelet at octave j
  • Y0(n): spectrum of the mother wavelet

• Average energy of X(t) around time instant 2jk and frequency 2-jn0, where n0 is the “central” frequency of the mother wavelet:

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