Recently, Zarowski and Kmpyvnytskyy developed a modified iterative cosinor algorithm (MICA) for the estimation of the parameters of sinusoidal signals with harmonics and subharmonics contaminated by AWGN, and derived the Cramer-Rao lower bound (CRLB) for the estimation of fundamental frequency component of such signals. However, their derivation was based on the assumption that the noise variance is known a priori. This paper presents a new derivation of CRLB bound for the case that the noise variance is unknown. The derivations also include the CRLB bounds for the estimation of harmonic and subharmonic amplitudes, noise variance as well as the SNR of the contaminated signal. Numerical simulation results are given to verify and interpret the derived CRLB bounds, together with the evaluation of estimation performance

In this paper we investigate the relation between the bandwidth and the energy ratio for sampled Daubechies (1992) scaling functions in digital communications. The energy ratio is defined as the energy in a specified band to the total energy. These characteristics are used to compare Daubechies scaling functions with Nyquist-type pulses having maximum energy ratio. It is shown that the sampled Daubechies scaling functions have energy ratio which are very close to optimum Nyquist-type pulses.

This article presents an approach to the initialization of the wavelet packet transform (WPT), which is a generalization of the discrete wavelet transform (DWT), by an extension of the interpolatory graphical display algorithm (IGDA). The exact computation of the WPT of functions that are piecewise constant on dyadic intervals is demonstrated. The method is for piecewise constant signals, as the details of how to do this do not appear to be readily available in the open literature. Furthermore, the solution is conveniently placed in a multirate signal processing framework.

The Berlekamp-Massey algorithm (BMA) (E. Berlekamp, 1968; J. Massey, 1969) is important in the decoding of Reed-Solomon (RS), and more generally, Bose-Chaudhuri-Hocquenghem (BCH) block error control codes. For a t-error correcting code the BMA has time complexity O(t/sup 2/) when implemented on a sequential computer. However, the BMA does not run efficiently on a parallel computer. The BMA can be mapped into the Schur BMA. The paper presents the implementation of the BMA and Schur BMA together on a linearly connected array of 2t processors. The resulting machine computes the error locator polynomial with a time complexity of O(t).>

Presents an improvement to Demho's (1988) lower bound on the smallest eigenvalue of a Hermitian positive-definite matrix. Unlike Dembo's bound the improved bound is always positive.>

A QR-type algorithm is developed to fit the delta autoregressive (DAR) model of R. Vijayan et al. to autocorrelation windowed sampled data. Vijayan et al. have developed Levinson-Durbin-type and Schur-type algorithms to compute the DAR model parameters when given a matrix Q/sub n/, which takes the place of the conventional autocorrelation matrix R/sub n/. They argue that the DAR model performs better than the conventional AR model for rapidly sampled data. There is not yet a theory on obtaining good estimates Q/sub n/ of from sampled data, contrasting with the well-developed theory for estimating R/sub n/. The proposed QR-type algorithm overcomes this problem by computing the DAR model parameters without the need for estimating Q/sub n/ directly. The AR algorithm proposed is a simple modification of the classical QR algorithm for the classical AR model due to C.P. Rialan and L.L. Scharf (1988).>

It has been stated by R.N. Gorgui-Naguib and R.A. King (1986) that the operations of addition and multiplication on Hensel codes originally defined by E.V. Krishnamurthy, T.M. Rao, and K. Subramanian (1975) are seriously in error in that it is possible to add/subtract or multiply Hensel codes and not get a valid Hensel code. It is shown that it is the presence of so-called invalid Farey fractions that results in the need to modify the original arithmetic operations. However, this also results in the Hensel codes becoming redundant. The authors show how to include the invalid Farey fractions such that it is possible to compute with their Hensel codings without the need to map back and forth between the rationals and their Hensel codings. This provides an alternative to the method of Gorgui-Naguib and King. Unfortunately, it turns out that Hensel codes of a large size will be needed in practice, even for relatively small problems.>