Spectral estimation based on discrete cosine transform and modified group delay

  • Authors:

  • S. V. Narasimhan;M. Harish

  • Affiliations:

  • Digital Signal Processing Systems Group, Aerospace Electronics and Systems Division, National Aerospace Laboratories, Bangalore, India;Digital Signal Processing Systems Group, Aerospace Electronics and Systems Division, National Aerospace Laboratories, Bangalore, India

  • Venue:
  • Signal Processing
  • Year:
  • 2006

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Abstract

This paper proposes a new spectral estimator based on discrete cosine transform (DCT) and modified group delay (MGD) function. This has been possible due to the establishment of a new Inverse DCT relation (DCT to discrete Fourier transform (DFT)) that preserves the desirable properties of DCT. This new estimator, which applies MGD to DFT derived from DCT (DCTMGD), provides a significant reduction in bias and variance and good signal detection ability; compared with those of MGD applied directly to DFT (DFTMGD). The DCT provides reduced bias (both in magnitude and frequency) that enables good signal detection ability and the MGD enables better variance reduction without any loss in frequency resolution. For two sinusoids in noise, the proposed method has an improvement in variance over that of DFTMGD by about 80% and 46% at signal to noise ratio of 20 and 0 dB, respectively. It is able to locate and resolve the spectral peaks even at SNR = -17 dB. For an autoregressive process, it reduces the root mean square error by 35% over that of DFTMGD. Also it has a significantly improved detectability as it brings out clearly the low level (23 dB below autoregressive peaks) sinusoid spectral peaks at a signal to noise ratio of 10 dB. Further, its performance is found to be better than that obtained by the Burg method.