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Two-dimensional minimum free energy autoregressive parametric modelling and spectral estimation

Dublin City University. School of Computing
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  • Digital Electronics
  • Digital Signal Processing
  • Multidimensional Levinson Method
  • Computer Science
  • Mathematics


We present a new high resolution spectral estimation method. This method is a 2-D extension of the Minimum Free Energy (MFE) parameter estimation technique based on extension of the multidimensional Levinson method Our 2-D MFE technique determines autoregressive (AR) models for 2-D fields MFE-AR models may be used for 2-D spectral estimation. The performance of the technique for spectral estimation of closely spaced 2-D sinusoids in white noise is demonstrated by numerical example. Experimental results from tests on spectral resolution, estimator bias and variance, and tolerance to change in signal processing temperature are examined. The effects on spectral estimation of signal to noise ratio, data set size, model size, autocorrelation type, and dynamic range difference are illustrated. The spectral estimates from combmed and single quarter plane estimates are contrasted. The results illustrate that MFE provides accurate low model order spectral estimation. The performance of the method is compared to the multidimensional Levinson, conventional transform, modified covariance (MCV), hybrid, and maximum entropy methods. It is seen that our MFE method provides superior spectral estimation over that which can be achieved with the Levinson algorithm with equivalent computational burden Superior spectral resolution is achieved at lower data set size than that provided by the Fourier transform method. In terms of spectral resolution, the MFE method performs just as well as the MCV method for snapshot data. It is seen that MFE provides spectral estimates that are as good as if not better than that provided by hybrid and maximum entropy methods. The computational expense, stability, and accuracy of spectral estimation over a number of independent simulation trials are examined for both MFE and MCV methods. The bias and variance statistics for MFE are comparable to those for MCV. However, the computational expense is far less than that of MCV and maximum likelihood methods. Models generated by our method give rise to stable and causal systems that are recursively computable. Hence they may also be used for correlation extension and for field modelling applications such as texture generation.

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