A New State Space-Based Approach for the Estimation of Two-Dimensional Frequencies and Its Parallel Implementations

摘要

In this paper, we present a new state space-based approach for the two-dimensional (2-D) frequency estimation problem which occurs in various 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. Two auxiliary Hankel-block-Hankel-like matrices are then introduced and from which the two frequency components can be derived via matrix factorizations along with frequency shifting properties. Although the algorithm can render high resolution frequency estimates, it also calls for lots of computations. To alleviate the high computational overhead required, a highly parallelizable implementation of it via the principle subband component (PSC) of some appropriately chosen transforms have been addressed as well. Such a PSC-based transform domain implementation 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 Fourier transform (DFT) or the Haar wavelet transform (HWT) be employed. As a consequence, such an approach of implementation can achieve substantial computational savings; meanwhile, as demonstrated by the provided simulation results, it still retains roughly the same performance as that of the original algorithm. A comparison with other existing algorithms has been made as well to justify the proposed approaches.