Browsing by Author "LIU, KJR"

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A UNIFIED SQUARE-ROOT-FREE APPROACH FOR QRD-BASED RECURSIVE LEAST-SQUARES ESTIMATION
(1993-03-01)
HSIEH, SF
;
LIU, KJR
;
YAO, K
;
電信工程研究所
;
Institute of Communications Engineering
Givens rotation is the most commonly used method in performing the QR decomposition (QRD) updating. The generic formula for these rotations requires explicit square-root (sqrt) computations which constitute a computational bottleneck and are quite undesirable from the practical VLSI circuit design point of view. So far, there has been more than ten known sqrt-free algorithms. In this correspondence, we provide a unified systematic approach for the sqrt-free Givens rotation. By properly choosing two parameters, mu and nu, all previously known sqrt-free, as well as new methods, are included in our unified approach. This unified treatment is also extended to the QRD-based recursive least squares (RLS) problem for optimum residual acquisition without sqrt operations.
DUAL-STATE SYSTOLIC ARCHITECTURES FOR UP DOWNDATING RLS ADAPTIVE FILTERING
(1992-06-01)
HSIEH, SF
;
LIU, KJR
;
YAO, K
;
電信工程研究所
;
Institute of Communications Engineering
We propose a dual-state systolic structure to perform joint up/down-dating operations encountered in windowed recursive least-squares (RLS) estimation problems. It is based on successively performing Givens rotations for updating and hyperbolic rotations for downdating. Due to data independency, a series of Givens and hyperbolic rotations can be interleaved and parallel processing can be achieved by alternatively performing updating and downdating both in time and space. This flip-flop nature of up/down-dating characterizes the feature of the dual-state systolic triarray. Efficient implementation on the evaluation of optimal residuals is also considered. This systolic architecture is promising for the VLSI implementation of fixed size sliding-window recursive least-squares estimations.
ESTIMATION OF MULTIPLE SINUSOIDAL FREQUENCIES USING TRUNCATED LEAST-SQUARES METHODS
(1993-02-01)
HSIEH, SF
;
LIU, KJR
;
YAO, K
;
電信工程研究所
;
Institute of Communications Engineering
Various SVD-based methods have been shown effective for resolving closely spaced frequencies. However, the massive computations required by SVD makes it unsuitable for real-time applications. To reduce the computational complexity, three truncated QR methods are proposed: 1) truncated QR without column pivoting (TQR); 2) truncated QR with reordered columns (TQRR); and 3) truncated QR with column pivoting (TQRP). It is demonstrated that many of the benefits of the SVD-based methods are achievable under the truncated QR methods with much lower computational cost. Based on the forward-backward linear prediction model, computer simulations and comparisons are provided for different truncation methods under various SNR's. Comparisons of asymptotic performance with large data samples are also given.
FAST ORTHOGONALIZATION ALGORITHM AND PARALLEL ARCHITECTURE FOR AR SPECTRAL ESTIMATION BASED ON FORWARD - BACKWARD LINEAR PREDICTION
(1993-03-01)
LIU, KJR
;
HSIEH, SF
;
電信工程研究所
;
Institute of Communications Engineering
The truncated QR methods have been shown to be comparable to the SVD-based methods for the sinusoidal frequency estimation based on the forward-backward linear prediction (FBLP) model. However, without exploiting the special structure of the FBLP matrix, the QR decomposition (QRD) of the FBLP matrix has the computational complexity on the order of 2(6m - n)n2/3 + O(n2) for a 2m x n FBLP matrix. Here we propose a fast algorithm to perform the QRD of the FBLP matrix by exploiting its special Toeplitz-Hankel form. The computational complexity is then reduced to 10n2 + 4mn + O(n). The fast algorithm can also be easily implemented onto a linear systolic array. The number of time steps required is further reduced to 2m + 5n - 4 by using the parallel implementation.