Authors' reply to “Comments on `Min-Norm interpretations andconsistency of MUSIC, MODE, and ML'”

For original article see Ephraim et al. (IEEE Trans. Signal Processing, vol.43, p.2937-42, December 1995). For comments to original article see Stoica and Ottersten (IEEE Trans. Signal Processing, vol.46, p.2262-3, August 1998). In the present reply to the comments the authors note that the signal subspace fitting approach of Ephraim et al. (1995) is different from that of Viberg and Ottersten (1991), and the consistency proof in Ephraim et al. contains the missing steps in the proofs of Viberg and Ottersten, and Stoica and Nehorai (1989). These facts, as well as the correctness of the results in Ephraim et al., are not disputed in Stoica and Ottersten. Stoica and Ottersten rather assert that the results in Ephraim et al. were either known or obvious     

Adaptive basis matrix for the morphological function processingopening and closing

A method for adaptation of the basis matrix of the gray-scale function processing (FP) opening and closing under the least mean square (LMS) error criterion is presented. We previously proposed the basis matrix for efficient representation of opening and closing (see IEEE Trans. Signal Processing, vol.43, p.3058-61, Dec. 1995 and IEEE Signal Processing Lett., vol.2, p.7-9, Jan. 1995). With this representation, the opening and closing operations are accomplished by a local matrix operation rather than cascade operation. Moreover, the analysis of the basis matrix shows that the basis matrix is skew symmetric, permitting to derive a simpler matrix representation for opening and closing operators. Furthermore, we propose an adaptation algorithm of the basis matrix for both opening and closing. The LMS and backpropagation algorithms are utilized for adaptation of the basis matrix. At each iteration of the adaptation process, the elements of the basis matrix are updated using the estimation of gradient to decrease the mean square error (MSE) between the desired signal and the actual filter output. Some results of optimal morphological filters applied to two-dimensional (2-D) images are presented.     

Fast algorithm for rate-based optimal error protection of embedded codes

Embedded image codes are very sensitive to channel noise because a single bit error can lead to an irreversible loss of synchronization between the encoder and the decoder. P.G. Sherwood and K. Zeger (see IEEE Signal Processing Lett., vol.4, p.191-8, 1997) introduced a powerful system that protects an embedded wavelet image code with a concatenation of a cyclic redundancy check coder for error detection and a rate-compatible punctured convolutional coder for error correction. For such systems, V. Chande and N. Farvardin (see IEEE J. Select. Areas Commun., vol.18, p.850-60, 2000) proposed an unequal error protection strategy that maximizes the expected number of correctly received source bits subject to a target transmission rate. Noting that an optimal strategy protects successive source blocks with the same channel code, we give an algorithm that accelerates the computation of the optimal strategy of Chande and Farvardin by finding an explicit formula for the number of occurrences of the same channel code. Experimental results with two competitive channel coders and a binary symmetric channel showed that the speed-up factor over the approach of Chande and Farvardin ranged from 2.82 to 44.76 for transmission rates between 0.25 and 2 bits per pixel.     

Comments on “Closed-form analysis of linearly constrainedCMA-based blind multiuser detector”

We point out that the proof of global convergence of LCCM detector is incorrect in the paper by Tang et al. (see ibid., vol.4, no.9, p.273-76, 2000). According to propositions presented in the paper by Xu and Feng (see Electron. Lett., vol.36, no.2, p.171-72, 2000), we further analyze the conditions for global convergence of LCCM detector, and give the low bound of constraint on the power of desired user     

Comments on “Discrete convolution by means of forward andbackward modeling”

The article by Porsani and Ulrych (see IEEE Trans. Acoust., Speech, Signal Processing, vol.37, no.1, p.1680, 1989) presented a method for calculating discrete convolution by means of a tap-delay line structure in conjunction with the Levinson-Durbin recursions as a new alternative to the conventional discrete convolution method. We show that care must be taken in implementing this algorithm     

A note on “On-line parameter identification algorithms basedon Householder transformation”

A detailed comparison of two on-line recursive least squares algorithms is presented. Liu's (see IEEE Trans. Signal Processing, vol.41, p.2863-71, Sept. 1993) fast on-line least squares algorithm based on Householder transformation and a stabilized version of a least squares algorithm based on the matrix pseudoinverse are considered     

Dynamic range of the detectable parameters for polynomial phasesignals using multiple-lag diversities in high-order ambiguity functions

Two lag diversities in the high-order ambiguity functions for single component polynomial phase signals (PPS) was explored by Zhou and Wang (see IEEE Signal Processing Lett., vol.4, p.240-42, 1997 and Signal Processing, vol.65, no.2, p.1452-55, 1998). The lag diversity enlarges the dynamic range of the detectable parameters for PPS. In this paper, we first find a connection between the above multiple-lag diversity problem and the multiple undersampling problem in the frequency detection using discrete Fourier transform (DFT). Using the connection and some results on the multiple undersampling problem we recently obtained, we prove that the dynamic range obtained by Zhou and Wang is already the maximal one for the detectable parameters for single-component PPS. Furthermore, the dynamic range for the detectable parameters for multicomponent PPS is given when multiple-lag diversities are used. We show that the maximal dynamic range is reached when the number of the lags in the high-order ambiguity function (HAF) is at least twice of the number of the single components in a multicomponent PPS. More lags than twice the number of single components do not increase the dynamic range     

Parameter estimation of exponentially damped sinusoids using higherorder statistics and matrix pencil

It is demonstrated that the higher-order-statistics-based algorithm proposed by C.K. Papadopoulos and C.L. Nikias (see IEEE Trans. Acoust. Speech Signal Process, vol.38, no.5, p.814-24, 1990) can be improved by using the matrix pencil approach of Y. Hua and T.K. Sarkar (see IEEE Trans. Acoust. Speech Signal Process., vol.38, no.8, p.1424-36, 1990). The matrix pencil algorithm is computationally more efficient than the Papadopoulos-Nikias algorithm since the computation of the K roots of the K-degree polynomial is not needed in the matrix pencil algorithm. Furthermore, it has been shown that the matrix pencil algorithm is less sensitive to noise than the Kumaresan-Tufts method     

New FFT bit-reversal algorithm

Presents a very short, simple, easy to understand bit-reversal algorithm for radix-2 fast Fourier transform (FFT), which is, furthermore, easily extendable to radix-M. In addition, when implemented together with Yong's (see IEEE Trans. Acoust., Speech, Signal Processing, vol.39, no.1O, p.2365-7, 1991) technique, the computing time is comparable to that of the fastest algorithms     

Comments on “Min-norm interpretations and consistency ofMUSIC, MODE, and ML”

For original paper see Ephraim et al. (IEEE Trans. Signal Processing, vol.43, p.2937-42, 1995 December). The results and interpretations obtained in the original paper are shown to be well known or obvious. Additionally, corrections to some misleading statements are presented     

Comments on “A comparison of two quantized state adaptivealgorithms”

The author presents a correction to an error in the paper of W.A. Sethares and C.R. Johnson (see IEEE Trans. Acoust. Speech Signal Processing, vol.37, no.1, p.138, Jan. 1989). A comparison is carried out between the quantized error (QE) and the quantized regressor (QReg) algorithms in the paper by Sethares and Johnson. However, an error in Theorem 1 leads to incorrect conclusions about the performance of the QE algorithm when using a quantizer with a dead zone     

Comment on the “Unnecessary assumption of statisticalindependence between reference signal and filter weights in feedforwardadaptive systems”

Minkoff (see IEEE Trans. Signal Processing, vol.45, p.2993-3004, 1997) presented a formulation in which the time-evolving weight-iteration equation for random signals is derived without the necessity of invoking the usual unsatisfactory assumption that is customarily made, namely, that the weights W and the reference signal X the weight-iteration equation are statistically independent. Minkoff neglected, however, to give a physical argument for it. That is, in this derivation, it is not necessary for W to be independent of X but only of XX which does not contain the phase information of X. The off-diagonal terms of XX contain only phase differences, which could be produced by an infinite number of different, arbitrary Xs     

Reply to “Comments on `A comparison of two quantized stateadaptive algorithms' ”

The author replies that Dr. Eweda is correct in noting that Theorem 1 does not apply to quantizers that incorporate a dead zone. However, the theorem, as stated in the original paper (see IEEE Trans. Acoust. Speech Signal Processing, vol.37, no.1, p.138, Jan. 1989) does not claim to apply to such quantizers     

High-order image subsampling using feedforward artificial neuralnetworks

We propose a method for high-order image subsampling using feedforward artificial neural networks (FANNs). In our method, the high-order subsampling process is decomposed into a sequence of first-order subsampling stages. The first stage employs a tridiagonally symmetrical FANN, which is obtained by applying the design algorithm introduced by Dumitras and Kossentini (see IEEE Trans. Signal Processing, vol.48, p.1446-55, 2000). The second stage employs a small fully connected FANN. The algorithm used to train both FANNs employs information about local edges (extracted using pattern matching) to perform effective subsampling of both high detail and smooth image areas. We show that our multistage first-order subsampling method achieves excellent speed-performance tradeoffs, and it consistently outperforms traditional lowpass filtering and subsampling methods both subjectively and objectively.     

Comments on “Theory and application of covariance matrixtapers for robust adaptive beamforming” [and reply]

For original paper see Guerci (IEEE Trans. Signal Processing, vol.47, p.977-85, 1999 April). Covariance matrix tapers and derivative constraints in the directions of jammers have been proposed for broadening the null in adaptive processing, thereby improving the algorithms' robustness. In this correspondence, the relationship between these two methods is explored. A reply is given in which Guerci makes some further points     

Correction to "Hidden Markov model multiarm bandits: a methodology for beam scheduling in multitarget tracking"

We have discovered an error in the return-to-state formulation of the HMM multiarmed bandit problem of Krishnamurthy and Evans (see IEEE Trans. Signal Processing, vol.49, p.2893-2908, Dec. 2001). This note outlines this error and describes a computationally simpler solution.     

Comments on “The Cramer-Rao lower bounds for signals withconstant amplitude and polynomial phase”

For original paper see IEEE Trans. Signal Processing, vol.39, p.749-52 (March 1991). Different expressions for the Cramer-Rao lower bounds (CRLBs) of constant amplitude polynomial phase signals embedded in white Gaussian noise appear in the literature. The present paper revisits the derivation of the bounds reported by Peleg and Porat (1991) and indicates that the resulting expressions depend on the interval over which the signal is defined. The proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds     

Author's reply by S. Wang and F. L. Teixeira

Wang and Teixeira reply to a comment (by An Ping Zhao, IEEE Microwave Wireless Comp. Lett., vol.14, no.5, p. 248-9, 2004) on their original paper (Wang and Teixeira, IEEE Microwave Wireless Comp. Lett., vol.13, p.72-4, 2003 February).     

Improvement in heuristic UTD diffraction coefficient

Holm (see IEEE Trans. Antennas Propag., vol.48, p.1211-19, 2000) has proposed a heuristic UTD diffraction coefficient for nonperfectly conducting wedges as an extension to the heuristic one given by Luebbers (see IEEE Trans. Antennas Propag., vol.32, p.77-6, 2000). The present work improves limitations of Holm's diffraction coefficient in the illumination region. The improved diffraction coefficient gives results that are very close to the Maliuzhinets (i.e. rigorous) diffraction coefficient. The improvement is valid for parallel and perpendicular field polarisations.