A NEW STATE SPACE-BASED APPROACH FOR THE ESTIMATION OF 2-DIMENSIONAL FREQUENCIES AND ITS PARALLEL IMPLEMENTATIONS

In this paper, we present a new state space-based approach for the two -dimensional (2-D) frequency estimation problem which occurs in variou s areas of signal processing and communication problems. The proposed method begins with the construction of a state space model associated with the noiseless data which contains a summation of 2-D harmonics. T wo auxiliary Hankel-block-Hankel-like matrices are then introduced and from which the two frequency components can be derived via matrix fac torizations along with frequency shifting properties. Although the alg orithm can render high resolution frequency estimates, it also calls f or lots of computations. To alleviate the high computational overhead required, a highly parallelizable implementation of it via the princip le subband component (PSC) of some appropriately chosen transforms hav e been addressed as well. Such a PSC-based transform domain implementa tion not only reduces the size of data needed to be processed, but it also suppresses the contaminated noise outside the subband of interest . To reduce the computational complexity induced in the transformation process, we also suggest that either the transform of the discrete Fo urier transform (DFT) or the Haar wavelet transform (HWT) be employed. As a consequence, such an approach of implementation can achieve subs tantial computational savings; meanwhile, as demonstrated by the provi ded simulation results, it still retains roughly the same performance as that of the original algorithm. A comparison with other existing al gorithms has been made as well to justify the proposed approaches.