A Simple Word Recognition Architecture Using Residue Number System Computation on a Systolic Array
Rashid Ansari, L. Bequillard, Willard L. Eastman · 1986
A procedure for obtaining IIR Hilbert transformers from generalized half-band filters is described. The relation of this result to the design procedure described by Gold et al. is explained. The filters are shown to be suited for specifications where the care-band for the Hilbert transformers is centered at 0.5~. Even when this condition is not satisfied, the proposed Hilbert transformers obtained by overde- sign may be preferable for implementation. Analytic solutions for non- casual Hilbert transformers and 90 phase shifters can be derived from special classes of classical low-pass filters. Numerical approximation can be used for designing IIR Hilbert transformers with right-sided impulse response. This gives us a single casual IIR filter (instead of a pair of 90 phase shifters) whose output is the approximate Hilbert transform of the delayed version of the input. Abstract-Fast least-squares algorithms draw their efficiency from a representation of least-squares parameters which is reduced to a min- imal number of variables. In the weighted form, they perform well on real hardware as long as that representation is correct. However, two facts can cause an incorrect representation to occur: the weighting fac- tor value can be incompatible with the input signal characteristics, and roundoff errors can accumulate. In this paper, a practical lower bound is derived for the weighting factor. Considering the so-called fast Kalman algorithm, it is shown that stability can be obtained by introducing a properly designed con- stant in the prediction error energy updating recursion. The process of roundoff error accumulation is then analyzed; it can be countered by properly weighting the difference between forward and backward prediction coefficients. The performance of the modified algorithm is assessed and extensions of the method to other algorithms and nonsta- tionary signals are discussed. Abstract-The application of the generalized least-squares (GLS) method to the estimation of the frequencies of sinusoids in additive colored noise is discussed. An algorithm based on the assumption that the parameter vector is symmetric, as well as on the adaptive contrac- tion of the poles of the noise whitening filter, is proposed. Expressions for the probability limit and the asymptotic variance of the estimates are derived for the single sinusoid case. Possible convergence points and the asymptotic behavior of the algorithm in the case of low SNR's are analyzed. Extensive simulation results show that the algorithm rep- resents a simple and reliable tool for practical applications.