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Space-time adaptive processing (STAP) is used for multiple-input multiple-output (MIMO) radar systems that have improved the spatial resolution for clutter. The STAP algorithm has computed the clutter space by using the prolate spheroidal wave functions (PSWF) and the block-diagonal property of the jammer covariance matrix.

A novel generalization of subspace-based blind channel identification methods in cyclic prefix (CP) systems is discussed. Results suggest the capability of the algorithm in performing blind identification using fewer received blocks.

The introduction of an adaptive beamformer that is robust against the direction-of-arrival (DOA) mismatch is discussed. Results suggest that the adaptive beamformer method possesses excellent signal-to-interference-plus-noise ratio performance and a complexity comparable to the standard minimum variance distortionless response (MVDR) beamformer.

The precoded vertical Bell labs layered space-time (V-BLAST) system is used in the case of frequency-selective multi-input multioutput (MIMO) channels. It is shown that the cyclic prefixing (CP)-based precoded V-BLAST system is good for the transceiver for MIMO frequency-selective channels when the channel information is available at the transmitter.

A theoretical problem arising in digital communication, namely the generalized signal richness preservation problem, is analyzed. Properties of Vandermonde-form preserving (VFP) matrices are studied and the necessary and sufficient conditions of the problem are found.

The concept of context-sensitive hidden Markov model (HMM) is introduced, which is capable of modeling strong pairwise correlations between distant symbols. Based on this model, dynamic programming algorithms that could be used for finding the optimal state sequence and for computing the probability of an observed symbol string is proposed.

Studies on theoretical issues about linear time invariant (LTI) systems that preserve signal richness are explored. Two particular definitions of signal richness are considered and the necessary and sufficient conditions under which an LTI system preserves the richness property are found.

A focus on the design of signal-adapted finite-impulse response (FIR) paraunitary (LPU) filter banks optimized for energy compaction (EC) is presented. The EC eptimal filter banks are shown to perform worse than common nonadapted filter banks for coding gain, contrary to intuition.

A method for approximating a multi-input multi-output (MIMO) transfer function by a causal finite-impulse response (FIR) paraunitary (PU) system in a weighted least-square sense is presented. An iterative algorithm is proposed that is greedy in the sense that the observed mean-square error at every iteration is guaranteed to not increase.

A study is conducted which proposed a modification of the traditional A Mutually Orthogonal Usercode-Receiver (AMOUR) system where the received continuous-time signal is oversampled by an integral or a rational amount. This idea leads to the concept of Fractionally Spaced AMOUR receivers that are derived for both integral and rational amounts of oversampling.

Several researchers present their study on the problem of estimating a probability density function (PDF) from measurements. A new-model based approach for modeling and estimating discrete probability density functions or probability mass functions is proposed.

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications. Index Terms--Channel-shortening equalizers, constrained filter design, eigenfilter, least-squares filter design.

An extension is presented of work involving the concept of biorthogonal partners.

We present a new low-complexity method for the design of channel shortening equalizers for discrete multitone modulation systems using the eigenfilter approach. In contrast to other such methods which require a Cholesky decomposition for each delay parameter value used, ours requires only one such decomposition. Simulation results show that our method performs nearly optimally in terms of observed bit rate. Index Terms--Channel-shortening equalizers, eigenfilter, fractionally spaced equalizers.

Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transforn (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This will be demonstrated with the help of numerical results for the case of the ADSL channel. Index Terms--Channel capacity, digital subscriber loops (DSL), discrete multitone (DMT) modulation, frequency division multiplexing (FDM), principal component filter banks (PCFB).

Tree-structured inverse halftoning is discussed. A new Look Up Table (LUT)-based halftoning method is discussed.

Halftoning is the rendition of continuous-tone pictures on displays, paper or other media that are capable of producing only two levels. In digital halftoning, we perform the gray scale to bilevel conversion digitally using software or hardware. In the last three decades, several algorithms have evolved for halftoning. Examples of algorithms include ordered dither, error diffusion, blue noise masks, green noise halftoning, direct binary search (DBS), and dot diffusion. In this paper, we first review some of the algorithms which have a direct bearing on our paper and then describe some of the more recent advances in the field. The dot-diffusion method for digital halftoning has the advantage of pixel-level parallelism unlike the error-diffusion method, which is a popular halftoning method. However, the image quality offered by error diffusion is still regarded as superior to most of the other known methods. We first review error diffusion and dot diffusion, and describe a recent method to improve the image quality of the dot-diffusion algorithm which takes advantage of the Human Visual System (HVS) function. Then, we discuss the inverse halftoning problem. Inverse halftoning is the reconstruction of a continuous tone image from its halftoned version. We give a brief review of the methods used in inverse halftoning, and discuss the advantadges of a recent inverse halftoning algorithm: Look-Up Table (LUT) Method for inverse halftoning. The method is extremely fast (no filtering is required) and the image quality achieved is comparable to the best methods known for inverse halftoning. The LUT inverse halftoning method does not depend on the specific properties of the halftoning method, and can be applied to any method. We then introduce LUT-based halftoning and tree-structured LUT (TLUT) halftoning. This algorithm involves only table look up operations but no arithmetic operations. We demonstrate how error-diffusion characteristics can be achieved with this method. Afterwards, our algorithm will be trained on halftones obtained by DBS which is an algorithm with high computational complexity. The complexity of TLUT halftoning is higher than that of error diffusion but much lower than that of the DBS algorithm. Thus, halftone image quality between that of error diffusion and DBS will be achieved depending on the size of tree structure in TLUT algorithm. Index Terms--DBS, dot diffusion, error diffusion, halftoning, HVS, inverse halftoning, LUT, ordered dither.

Multiple input, multiple output (MIMO) biorthogonal partners, which arise naturally in many signal processing applications such as MIMO channel equalization and multiwavelet theory, are discussed. Theoretical aspects are considered, and several applications are described.

A simplified, all-FIR (Finite Impulse Response) implementation is proposed, for signal interpolation based on piecewise polynomial models. The new implementation is advantageous because of increased flexibility.

Look-up table (LUT)-based methods for inverse halftoning of images are proposed. Performance is demonstrated on error-diffused images and ordered-dithered images, and LUT inverse halftoning is extended to color halftones.

Optimization of filter banks for specific input statistics has been of interest in the theory and practice of subband coding. For the case of orthonormal filter banks with infinite order and uniform decimation, the problem has been completely solved in recent years. For the case of biorthogonal filter banks, significant progress has been made recently, although a number of issues still remain to be addressed. In this paper we briefly review the orthonormal case, and then present several new results for the biorthogonal case. All discussions pertain to the infinite order (ideal filter) case. The current status of research as well as some of the unsolved problems are described.

A set of required and sufficient conditions for the coding-gain optimality of an orthonormal subband coder for a particular input statistics was derived. Several theoretical characteristics of optimal compaction filters and optimal subband coders were derived, particularly those involving behavior as the number of subbands decreases. Substantial theoretical differences between optimum subband coders, transform coders and predictive coders were observed.

Innovative techniques can be utilized in designing optimum finite impulse response (FIR) compaction filters which are suitable for a restricted class of signals. One of the methods utilizes Levinson recursion and two spectral factorization of half the filter order which may yield a two-channel FIR filter bank that optimizes the coding gain under conventional quantization noise assumptions while the window method may provide efficient suboptimal design. The methods are useful in important signal processing applications.

It is known that a continuous time signal [Chi](t) with Fourier transform X([Nu]) band-limited to [absolute value of [Nu]] [less than] [Theta]/2 can be reconstructed from its samples [Chi]([T.sub.o] n) with [T.sub.o] = 2[Pi]/[Theta]. In the case that x([Nu]) consists of two bands and is band-limited to [[Nu].sub.o] [less than] [absolute value of [Nu]] [less than] [[Nu].sub.o] + [Theta] 2, successful reconstruction of [Pi](t) from [Pi]([T.sub.o] n) requires an additional condition on the band positions. When the two bands are not located properly, Kohlenberg showed that we can use two sets of uniform samples, [Pi]([2T.sub.o]n) and [Pi]([2T.sub.o] n+[d.sub.1]), with average sampling period [T.sub.o], to recover [Pi](t). Because two sets of uniform samples are employed, this sampling scheme is called Periodically Nonuniform Sampling of second order [PNS(2)]. In this paper, we show that PNS(2) can be generalized and applied to a wider class. Also, Periodically Nonuniform Sampling of Lth-order [PNS(L)] will be developed and used to recover a broader class of band-limited signals. Further generalizations will be made to the two-dimensional case and discrete time case.

A study was conducted on the derivation of anticausal inverse structures corresponding to several standard IIE filter structures such as the direct-form, cascade-form, coupled-form and the entire family of IIR lattice structures. The notion of a causal dual was found convenient in the derivation. The findings indicate that the causal dual inherits the limit-cycle free property of the original structure in some cases.

We consider the optimization of pre- and postfilters surrounding a quantization system. The goal is to optimize the filters such that the mean square error is minimized under the key constraint that the quantization noise variance is directly proportional to the variance of the quantization system input. Unlike some previous work, the postfilter is not restricted to be the inverse of the prefilter. With no order constraint on the filters, we present closed-form solutions for the optimum pre- and postfilters when the quantization system is a uniform quantizer. Using these optimum solutions, we obtain a coding gain expression for the system under study. The coding gain expression clearly indicates that, at high bit rates, there is no loss in generality in restricting the postfilter to be the inverse of the prefilter. We then repeat the same analysis with first-order preand postfilters in the form 1 + [[Alpha]z.sup.-1] and 1/(1+[[Alpha]z.sup.-1]). In specific, we study two cases: 1) FIR prefilter, IIR postfilter and 2) fIR prefilter, FIR postfilter. For each case, we obtain a mean square error expression, optimize the coefficients [Alpha] and [Gamma] and provide some examples where we compare the coding gain performance with the case of [Alpha] = [Gamma]. In the last section, we assume that the quantization system is an orthonormal perfect reconstruction filter bank. To apply the optimum pre- and postfilters derived earlier, the output of the filter bank must be wide-sense stationary WSS which, in general, is not true. We provide two theorems, each under a different set of assumptions, that guarantee the wide sense stationarity of the filter bank output. We then propose a suboptimum procedure to increase the coding gain of the orthonormal filter bank. Index Terms - Half-whitening scheme, noise shaping, optimum pre- and postfiltering, subband coding.

The factorability of linear time-varying (LTV) lossless filters and filter banks was investigated. Degree-one lossless LTV systems were characterized and were found decomposable into a unitary matrix followed by a lossless dyadic-based LTV based system. Several properties of lossless dyadic-based systems were cited significant in the factorization of lossless linear time-varying systems.

The concept of paraunitary filter banks in GF(q) with q prime is investigated. Findings indicate that all unitary matrices in GF(q) are factorizable in terms of Householder-like matrices and permutation matrices and the class of first-order paraunitary matrices or the lapped orthogonal transform in finite fields can always be represented as a product of degree-one or degree-two building blocks.

The current sampling theory for wavelet subspaces is extended in several directions. Periodically nonuniform sampling, sampling of a function and its derivatives, oversampling, multiband sampling and reconstruction from local averages are studied. All these problems are handled in a unified way using the perfect reconstruction filter bank theory. Some of the suggested methods can be employed for efficient calculation of inner products in multiresolution analysis.

A polyphase approach to time-varying filter banks (TVFB) unravels some unusual characteristics that are unlike those exhibited by conventional LTI filter banks. Analysis of a perfect reconstruction (PR) TVFB shows the losslessness of analysis bank is not necessarily due to the synthesis bank. A nonlossless system may be generated by substituting the delay 1/z in a lossless linear time-variant system with 1/z raised to Lth power. Interchange of the analysis and synthesis filters not only cancels the PR property, but also destroys the ability to generate a discrete-time basis.

The statistical properties of the error in uniform scalar quantization have been analyzed by a number of authors in the past, and is a well-understood topic today. The analysis has also been extended to the case of dithered quantizers, and the advantages and limitations of dithering have been studied and well documented in the literature. Lattice vector quantization is a natural extension into multiple dimensions of the uniform scalar quantization. Accordingly, there is a natural extension of the analysis of the quantization error. It is the purpose of this paper to present this extension and to elaborate on some of the new aspects that come with multiple dimensions. We show that, analogous to the one-dimensional case, the quantization error vector can be rendered independent of the input in subtractive vector-dithering. In this case, the total mean square error is a function of only the underlying lattice and there are lattices that minimize this error. We give a necessary condition on such lattices. In nonsubtractive vector dithering, we show how to render moments of the error vector independent of the input by using appropriate dither random vectors. These results can readily be applied for the case of wide sense stationary (WSS) vector random processes, by use of iid dither sequences. We consider the problem of pre- and post-filtering around a dithered lattice quantizer, and show how these filters should be designed in order to minimize the overall quantization error in the mean square sense. For the special case where the WSS vector process is obtained by blocking a WSS scalar process, the optimum prefilter matrix reduces to the blocked version of the well-known scalar half-whitening filter.

A four parallelogram filter bank is a type of two-dimensional filter bank in which the analysis and synthesis filters are supported by four parallelograms. The choice of integer matrix and the location of the four parallelograms control the type of configuration for these filter banks. Derivation of design condition for analysis and synthesis filters shows that a unique category of configurations exists for four-parallelogram filter banks. The configurations in this category are obtained by designing low-cost filter banks.

The passbands of each analysis filter in two-parallelogram filter banks consist of two parallelograms. Parallelogram cells partition the frequency plane. These filter banks can have either edge permissibility or vertex permissibility but not both. This keeps the stopband attenuation of the filters at a low level. The cosine-modulated filter bank (CMFB) is a special type of two-parallelogram filter bank in which the analysis and synthesis filters are cosine-modulated versions of a parallelogram-supported prototype. The conditions for the reconstruction of the CMFB are derived.

Pre and postfiltering achieve significant improvement in coding gain of paraunitary filter banks. Such filters for optimal coding gain are determined by the power spectrum of the input process. However, the optimized coding gain depends on the prefilter and the paraunitary filter bank. The optimal design of filters in a prefiltered paraunitary filter bank is discussed.

The analysis and synthesis filters of maximally decimated FIR cosine modulated filter banks have a linear phase within a new design system for these filters. The coding gain of the system is comparable to that of a traditional M-channel system due to the use of two band-pass filters with a similar passband support. The system design can have either the approximate reconstruction property or perfect reconstruction property. The system has good attenuation characteristics, and is efficient.

The system-theoretic properties of discrete time transfer inversed matrices are classified according to the types of inverses, particularly of the CAusal FIR matrices with AntiCAusal FIR inverses (cafacafi), for characterization of FIR perfect reconstruction (PR) filter banks. A specially developed biorthogonal lapped transform (BOLT) system solves the introduced general degree-one cafacafi building block factorization. Its various applications in factorization process have been demonstrated.

Perfect reconstruction filter banks properties can be classified based on the nature of the inverse of the polyphase matrix E(z) in a maximally decimated filter bank with identical decimation ratios for all channels. The causal polyphase matrices with anticausal inverses plays a key role in the filter bank theory. The factorization of biorthogonal FIR filter banks is one application for the results.