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A New State SpaceBased Approach for the Estimation of TwoDimensional Frequencies and Its Parallel Implementations
Yi CHU WenHsien FANG ShunHsyung CHANG
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E80A
No.6
pp.10991108 Publication Date: 1997/06/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: PAPER Category: Digital Signal Processing Keyword: frequency estimation, state space model, parallel algorithms, discrete Fourier transform, discrete Haar wavelet transform,
Full Text: PDF>>
Summary:
In this paper, we present a new state spacebased approach for the twodimensional (2D) 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 2D harmonics. Two auxiliary HankelblockHankellike 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 PSCbased 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.

