Lag-windowing and multiple-data-windowing are roughly equivalent for smooth spectrum estimation

  • Authors:

  • M.L. McCloud;L.L. Scharf;C.T. Mullis

  • Affiliations:

  • Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA;-;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 1999

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Abstract

There is no fundamental difference between lag-windowing a correlation sequence and multiple-windowing a data sequence when the objective is to reduce the mean-squared error of a spectrum estimator. By analyzing the approximate low-rank factorization of a bandlimiting Toeplitz operator, we find that lag-windowed (or spectrally smoothed) spectrum estimators have multiple-data-windowed implementations. This makes the Blackman-Tukey-Grenander-Rosenblatt spectrogram equivalent to the Thomson spectrum estimator (and vice-versa), meaning BTGR spectrograms may be implemented in a multichannel filterbank version of the Thomson estimator.