Two-dimensional spectral estimation
JAMES A. CADZOW, Koji Ogino · IEEE Transactions on Acoustics Speech and Signal Processing · 1981
In this paper, effective methods for generating two-dimensional quarter-plane causal autoregressive (AR) and autoregressive moving average (ARMA) spectral estimation models are developed. These procedures are found to provide super resolution capabilities when compared to other more classical methods such as the Fourier transform. The ARMA method involves manipulation of the model equation\sum\min{k = 0}\max{p_{1}} \sum\min{k = 0}\max{p_{2}} a_{km}x(n_{1} - k, n_{2} - m) = \sum\min{k = 0}\max{q_{1}} \sum\min{k = 0}\max{q_{2}} b_{km}\epsilon(n_{1} - k, n_{2} - m)and utilizes the given finite set of observationsx(n_{1}, n_{2})for1 \leq n_{1} \leq N_{1},1 \leq n_{2} \leq N_{2}. In the above relationship, the random excitation{\epsilon(n_{1}, n_{2})}is taken to be white. This ARMA model's autoregressive akmcoefficients are selected to minimize a weighted least-squares criterion composed of error elements while the moving average bkmcoefficients are obtained using an alternative approach. The spectral estimation performance of the AR and ARMA methods will be empirically demonstrated by considering the problem of resolving two sinusoids embedded in noise.