In this paper, we propose a blind channel estimation algorithm for amplify-and-forward two-way relay networks (AF-TWRN). The orthogonal frequency division multiplexing (OFDM) modulation is adopted for frequency selective channel. The channels are estimated in two steps. First the cascaded channel causing the self-interference is estimated using a proposed power reduction method. Then the other cascaded channel from source to destination is estimated by subspace method. Closed form formulas are derived and the numerical results are provided.

In this paper, a new algorithm based on cyclic prefix (CP) is proposed for blind carrier frequency offset (CFO) estimation in orthogonal frequency division multiplexing (OFDM) transmission over multipath channels. Like other CP-based methods, the proposed method enjoys low complexity. The proposed method is very robust to the symbol timing synchronization error. Closed-form formulas for CFO estimates are derived. In addition, we also carry out the theoretical mean-square-error analysis and derive the Cramer-Rao bound. Simulation results show that the proposed method performs very well.

The estimation of carrier frequency offset (CFO) and in-phase and quadrature-phase (I/Q) imbalance is an important issue in the study of the orthogonal frequency division multiplexing (OFDM) systems. In our recent work [6], we have proposed a blind algorithm for the estimation of CFO in the absence of I/Q imbalance. In this paper, a blind algorithm is introduced for the estimation of I/Q parameter in the presence of CFO. The proposed method does not need to know the channel and CFO value. Moreover a closed form formula for the I/Q parameter is derived and thus the algorithm has low complexity. Simulation results show that the proposed method performs very well. Combining the proposed method and our method in [6], we can solve the joint estimation problem of I/Q and CFO.

Two novel subspace-based blind channel estimation methods for orthogonally coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with more than two transmit antennas are proposed in this paper. The proposed methods exploit the null space induced by the orthogonal space-time block codes (OSTBC). They can be applied to systems with one or more receive antennas. Simulation results show that accurate estimates can be obtained.

The estimation of carrier frequency offset (CFO) is an important issue in the study of the orthogonal frequency division multiplexing (OFDM) systems. In the past, many CFO estimation methods have been proposed. In this paper, we propose a new blind CFO estimation for OFDM systems based on the so-called remodulated received vectors [8]. The CFO estimate is given by a closed form formula. The proposed method has very low complexity and its performance is robust to different modulation symbols and the presence of virtual carriers.

In the last decade, several subspace-based algorithms for blind channel identification in zero-padded systems were introduced. These subspace-based methods are attractive because highly accurate estimates of the channel can be obtained by using only a few received blocks. However, they do not work when applied to the zero-padded orthogonal frequency division multiplexing systems (ZP-OFDM) with virtual carriers. In this paper, we propose two improvements on an earlier subspace-based blind channel estimation method for such systems. Firstly, we introduce a simple noise weighting approach. Unlike most of the earlier methods, the proposed weighting matrix is diagonal and it is independent of the channel noise variance and SNR. By doing so, the performance of previous work is significantly enhanced. Secondly, we extend the blind estimation method to ZP-OFDM systems with virtual carriers. Simulations are carried out to demonstrate the merits of the proposed method.

Recently, a blind subspace channel estimation algorithm in which using only a few received OFDM blocks is proposed. Based on this earlier work, we introduce a novel subspace-based blind carrier frequency offset (CFO) estimation method for OFDM systems. The CFO is obtained by solving the nullspace of the proposed rank-reduced matrix and the CFO estimate is given in closed form. Moreover, we do not make the assumption that the modulation symbols are white or constant-modulus. Simulation results show that the proposed method performs better than the existing methods.

In this paper, we study the estimation of carrier frequency offset (CFO) in the presence of the receiver in-phase and quadrature-phase (I/Q) imbalance for orthogonal frequency division multiplexing (OFDM) systems. By minimizing the energy of the samples on the virtual subcarriers, our proposed algorithm can jointly estimate the CFO and I/Q parameters using one OFDM block. When the CFO is small, a closed-form solution can be obtained. Simulation results show that our proposed method can provide a good performance for both of the I/Q and CFO estimation and it compares favorably with a recent method.

The estimation of carrier frequency offset (CFO) is an important issue for OFDM systems. Many CFO estimation methods have been proposed in the past. In particular, two ESPRIT-based methods were introduced for blind CFO estimations. These ESPRIT-based methods can provide satisfactory performance at a reasonable implementation cost. In this paper, we propose a least-squares (LS) algorithm for improving the performance of these ESPRIT-based methods. Simulation results show that the proposed LS algorithm, although very simple, can significantly improve the accuracy of CFO estimation.

In this letter, we jointly consider statistical precoding and statistical bit allocation for correlated MIMO channels. Given the statistics of the channel, we derive statistical BER bounds for high and low SNR ranges. Based on the BER bounds, statistical precoder and statistical bit allocation are designed. The statistical precoder helps to expose the statistical difference among the subchannels, which is then exploited by bit allocation. Moreover, we will incorporate bit allocation in determining detection ordering for the decision feedback receiver and present a suboptimal ordering for minimizing the worst subchannel error rate. The suboptimal solution can be implemented efficiently by modifying existing fast algorithms developed for uniform bit allocation. Although the statistical precoder and bit allocation are designed for high and low SNR ranges, very good performance can be achieved for all SNR. Simulations show that the performance of the proposed system is comparable to one that has instantaneous feedback rate of around 4 bits per channel.

Carrier frequency offset (CFO) and in-phase and quadrature-phase (I/Q) imbalance are two of the common front-end impairments in low-cost communication devices. It is known that CFO can cause significant performance degradation in multi-carrier modulation (MCM) systems. Also, the existence of the I/Q imbalance usually reduces the accuracy of CFO estimation. In this paper, we propose a new data-aided scheme for the joint estimation of CFO and I/Q imbalance using simple matrix formulation. The proposed algorithms utilize only the periodicity of the generalized periodic pilot (GPP). They do not need to know the channel impulse response and the exact values of the training sequence. Moreover, our method has a low complexity and its performance compares favorably with the existing methods.

Carrier frequency offset (CFO) and in-phase/quadrature-phase (I/Q) imbalance are two major impairments of the wideband direct-conversion receivers. They can cause significant performance degradation in multi-carrier modulation systems. In this paper, we propose a new two-step algorithm for estimating the parameters of both impairments based on generalized periodic pilot (GPP). Simulation results show that the proposed method has a good performance. Furthermore, the complexity of our algorithm is lower than the existing methods.

In this paper, we propose an efficient iterative algorithm for finding the minimum sampling frequency for a signal that consists of multiple bandpass signals. This finds important application in software radio where it is desirable to down-convert multiple bandpass signals simultaneously. We will derive a new set of conditions for alias-free sampling for signals that contain multi-band signals. The conditions can be easily examined with few computations. The minimum sampling frequency can be found by iteratively increasing the sampling frequency to meet the alias-free conditions. The simulations demonstrate that the proposed method requires a much lower complexity than existing algorithms.

The estimation of carrier frequency offset (CFO) is an important topic in broadband communication systems. It is known that the accuracy of CFO estimation will be affected by the existence of the in-phase and quadrature-phase (I/Q) imbalance. This paper proposes a novel algorithm for CFO estimation in the presence of I/Q imbalance. The estimation problem is solved by using a simple matrix approach. It exploits only the periodicity of the training sequence, and it does not need the information about the channel impulse response and the exact values of training sequence. Simulation results show that our method is robust to both the noise and the various values of CFO, and it compares favorably with the existing methods.

In this paper, we study the joint estimation of inphase and quadrature-phase (I/Q) imbalance, carrier frequency offset (CFO), and channel response for multiple-input multipleoutput (MIMO) orthogonal frequency division multiplexing (OFDM) systems using training sequences. A new concept called channel residual energy (CRE) is introduced. We show that by minimizing the CRE, we can jointly estimate the I/Q imbalance and CFO without knowing the channel response. The proposed method needs only one OFDM block for training and the training symbols can be arbitrary. Moreover when the training block consists of two repeated sequences, a low complexity two-step approach is proposed to solve the joint estimation problem. Simulation results show that the mean-squared error (MSE) of the proposed method is close to the Cramer-Rao bound (CRB).

In this paper, we study the joint estimation of I/Q imbalance, CFO and channel response for OFDM systems. Using two repeated OFDM blocks for training, we propose a new method to solve the joint estimation problem. The implementation complexity is low. Simulation results show that the proposed method has a good performance and its BER is very close to the ideal case where all the parameters are known perfectly at the receiver.

In this paper, we study the problem of channel estimation in the presence of the transmitter and receiver inphase and quadrature-phase (I/Q) mismatches for orthogonality frequency division multiplexing (OFDM) systems. A new concept called channel residual energy (CRE) is introduced. We show that by minimizing CRE, we can jointly estimate the transmitter and receiver I/Q mismatches without knowing the channel information. The optimal solution is given in closed form. Once we have the I/Q parameters, an estimate of the channel response can be obtained by simple substitution. The proposed method needs only one OFDM block for training and the training data can be arbitrary. Simulation results show that the proposed method can achieve a good performance.

In this paper, we first introduce a new method for joint estimation of IQ imbalance and channel response in OFDM systems under the assumption of perfect frame synchronization. The proposed method needs only one OFDM block for training and the solution is given in closed form. Then the method is applied to the scenario when the OFDM frame is not synchronized. A reduced complexity algorithm is derived. With a relatively low complexity, the proposed method can accurately estimate the frame starting position, the IQ imbalance and the channel response simultaneously. Simulation results show that the bit error rate (BER) performance of the proposed method is very close to the ideal case when all these parameters are known perfectly at the receiver.

In this paper a time-domain method for joint estimation of in-phase and quadrature-phase (IQ) imbalance, direct current (DC) offset and channel response for orthogonal frequency division multiplexing (OFDM) system is proposed. Using the fact that in an OFDM system the block size is usually much larger than the cyclic prefix length, we show that without knowing the channel impulse response, we are able to accurately estimate the IQ mismatch and DC offset, from which the channel response can be obtained. Only one OFDM block is needed for training. Simulation results demonstrate that the performance of the proposed method is very close to the ideal case when IQ mismatch, DC offset and channel response are perfectly known at the receiver.

Recently it was shown that a linear precoder can greatly improve the performance of OFDM systems. In this paper, we study linear precoder for space-time coded OFDM (ST-OFDM) system for multiple antenna transmission. The effect of a linear precoder is analyzed when the ST-OFDM system suffers from intersymbol interference caused by undetected channel variations. For QPSK modulation, the optimal precoder that minimizes the bit error rate (BER) is derived. It is found that the optimal precoder is channel independent. Simulation results show that the optimal precoder can significantly lower the BER of ST-OFDM system.

In this paper, we propose a frequency domain based design method for designing TEQ (time domain equalizer) for DSL (digital subscriber loops) applications. In DSL applications, usually frequency division multiplexing is used to separate the upstream and downstream signals. In either direction of transmission, some of the frequency bands are not used for transmission. Interference is formulated and minimized in the frequency domain to take advantage of the unused frequency bands. The frequency domain approach allows us to have a more direct control over the frequency response of the resulting TEQ, which is crucial in the final achievable transmission bit rates. The simulation examples demonstrate that the proposed method shortens the channel effectively and very good transmission bit rates can be achieved.

In this paper, we consider the cosine modulated filter bank (CMFB) transceiver for unknown channels. Although it is a CMFB transceiver, the only channel dependent part of the transceiver is a set of scalar multipliers at the receiver, like the OFDM. We show how to optimize the transmit and receive prototype filters so that the signal to interference ratio (SIR) is maximized. Moreover a new objective function that can incorporate the frequency response criteria is proposed. Simulation results show that we can obtain CMFB transceivers with high SIR values and good frequency responses.

In this paper, we propose a semi-blind time domain equalizer (TEQ) design method for VDSL systems. In the VDSL system, frequency division duplex is used to separate upstream and downstream signals. In downstream or upstream transmission, only half the tones carry data and the other half are null tones. The proposed semi-blind method exploits the null tones of VDSL training symbols. It does not require the channel impulse response nor the channel noise statistics, like all eigen approaches proposed earlier. An example is given to demonstrate that the proposed TEQ design method can effectively shorten the channel impulse responses for VDSL applications.

Discrete multitone (DMT) modulation has been widely adopted for wideband transmission over digital subscriber loop (DSL) channels. In the conventional DMT system, the transmitting filters are the DFT filters. DFT filters suffer from poor frequency responses. Hence, the resulting transmit signal has a large spectral sidelobe and its power spectral density (PSD) decays at a rate of 1/f only. In this paper, we propose a modified DMT scheme with improved transmitting filters. In the proposed system, shaping filters are applied to improve the frequency responses of the transmitting filters. Moreover, an efficient implementation of the proposed system is derived. Experiment shows that for VDSL applications, the proposed system has a very satisfactory spectral efficiency.

The transmitter output of OFDM or DMT systems with a rectangular window is known to have large spectral sidelobes. Windowing and pulse shaping have been proposed to reduce spectral leakage in the literature. If no extra cyclic prefix is available, windowing at the transmitter requires additional post-processing equalization at the receiver. In this paper, we design optimal windows with minimum spectral leakage. Moreover, we show that the post processing affects the SNR at the receiver and the resulting SNR can be given in a closed form. Furthermore, we demonstrate that we can have a good trade-off between SNR and spectral leakage.

In this paper, we study DFT-bank transceivers with filter length longer than the block size. We show how to optimize the DFT-bank transceiver so that both the intra-band and cross-band interferences are minimized for unknown multipath channels. No costly post processing technique is needed and the only channel dependent part is a set of one-tap equalizers at the receiver. The optimization problem is formulated as a Rayleigh-Ritz ratio whose solution is well-known. Experiments are carried out for transmission over random multipath channels and the results show that satisfactory signal-to-interference ratio performance can be obtained.

In this paper we consider window designs for DFT (discrete Fourier transform) based multicarrier transceivers without using extra cyclic prefix. As in previous works of window designs for DFT based transceiver, a post processing matrix, generally channel dependent, is needed to have a zero forcing receiver. We show that post processing is channel independent if and only if the window itself has the cyclic prefixed property. We design optimal windows with minimum spectral leakage subject to the cyclic-prefixed condition. Moreover, we analyze how post processing affects SNR (signal to noise ratio) at the receiver, an aspect that is hot considered in most of the earlier works. The resulting SNR can be given in a closed form. Join optimization of spectral leakage and SNR are also considered. Furthermore, examples demonstrate that we can have a significant reduction in spectral leakage at the cost of a small SNR penalty.

In this paper, we proposed using MFCC coefficients (mel-scaled cepstral coefficients) and a simple but efficient classifying method: vector quantification (VQ) to perform speaker-dependent emotion recognition. Many other features: energy, pitch, zero crossing, phonetic rate, LPC... and their derivatives are also tested and combined with MFCC coefficients in order to find the best combination. Other models, GMM and HMM (discrete and continuous hidden Markov model), are studied as well in the hope that the use of continuous distribution and the temporal evolution of this set of features will improve the quality of emotion recognition. The accuracy recognizing five different emotions exceeds 80% by using only MFCC coefficients with VQ model. This is a simple but efficient approach, the result is even much better than those obtained with the same database in human evaluations by listening and judging without returning permission nor comparisons between sentences (Inger Samso Engberg and Anya Varnich Hansen, 2001).

In this letter, we propose a new passband criterion for eigenfilters. Instead of choosing the response at a particular frequency in the passband as the desired response, the new criterion chooses the average passband gain as the desired response. The new criterion does not increase the design cost. Simulations show that the proposed criterion leads to better filters both in least square sense and in minimax sense.

The single carrier system with cyclic prefix (SC-CP) has been demonstrated to outperform the OFDM system through simulations. In this paper, we consider minimum mean squared error (MMSE) receivers for the SC-CP system. We show analytically that, for uncoded QPSK symbols, the SC-CP system with an MMSE receiver has a smaller bit error rate (BER) than the OFDM system for all SNR.

In this paper, we generalize the Hadamard transform to the case of lapped transform. A matrix A(z) is a lapped Hadamard transform if it satisfies A/sup T/(z/sup -1/)A(z)=/spl alpha/I for some integer /spl alpha/ and all the entries of its coefficient matrices are /spl plusmn/1. Many methods have been proposed to construct lapped Hadamard matrices. In this paper, we study these matrices using the theory of paraunitary filter bank. This approach not only greatly simplifies the analysis of lapped Hadamard transform but also gives rise to new construction methods that can generate a much wider class of lapped Hadamard matrices.

We consider the minimization of bit error rate (BER) for OFDM systems with orthogonal precoders. For low SNR, we show that the conventional OFDM system is the optimal solution and the optimal precoder is the identity matrix. For high SNR, corresponding to a relatively practical range of BER, there are channel independent solutions for optimal precoders. One such solution is the DFT matrix and the resulting optimal transceiver becomes the single carrier transmission system. Furthermore, in this case the conventional OFDM system has the largest BER among all OFDM systems with orthogonal precoders.

The pseudocirculant matrices have been found to be a very useful tool in the analysis and design of communication systems, e.g., precoding systems and discrete multitone transceivers. In these systems, a scalar channel P(z) is recast into a pseudocirculant channel matrix. Many important channel properties have been derived from the Smith form and the decomposition of pseudocirculants. In this letter, we will show that the Smith form of a pseudocirculant matrix can be given in terms of the zeros of the underlying finite-impulse response (FIR) channel P(z). Once the zeros of P(z) are known, the Smith form of the corresponding pseudocirculant matrix can be obtained in closed form.

It is well-known that the Karhunen-Loeve transform (KLT) is optimal for white noise suppression. Akkarakaran and Vaidyanathan (see IEEE Trans. Signal Processing, vol.49, no.1, p.100-114, 2001) showed that for the case of colored noise, if both the noise and signal have a common KLT, then the KLT is optimal for subband noise suppression. We derive the optimal transform (not restricting to the class of unitary transforms) for the noise suppression problem when the signal and noise have arbitrary spectrum.

There has been great interest in the design of DMT (discrete multitone) transceivers. An M-band DMT transceiver is called block based if the transmitter and the receiver consist of constant matrices. The commonly used DMT systems are mostly block based, e.g., the DFT based system used in transmission over digital subscriber lines. For an FIR channel of order L, it is known that redundancy of length L enables the receiver to cancel ISI completely. Such a scheme allow us to trade bandwidth for ISI cancellation. In block based DMT (BDMT) systems, the redundancy K is typically chosen to be the same as the order of the channel L. We consider BDMT transceiver with redundancy K /spl les/ L. With the reduced redundancy better bandwidth efficiency can be obtained as demonstrated by examples. Furthermore minimum redundancy for BDMT systems are derived and the transceivers are parameterized whenever intersymbol interference (ISI) solutions exist.

The design of optimal DMT transceivers for distorted channel with colored noise has been of great interest. Of particular interest is the class of block based DMT (BDMT), where the transmitter and the receiver consist of constant matrices. For a given channel and channel noise spectrum, the optimal DBMT transceiver that minimizes the transmission power for a fixed probability of error and transmission rate is derived. The optimal biorthogonal transmitter is in fact orthogonal. That is, there is no loss of generality in using the orthogonal transmitter for the design optimal BDMT.

Motion compensation using the optimal full search algorithm is often too computationally heavy for real-time implementation. Many suboptimal fast search algorithms have been proposed. In particular, Liu and Zaccarin (1993) proposed the alternating subsampling search algorithm (ASSA). The ASSA reduces the computation by subsampling the pixels instead of limiting the search locations. It was shown that ASSA has nearly the same MSE performance as the full search but its complexity is only 1/4 of the full search. We generalize the idea to the multi-stage case. Simulation results show that the proposed algorithm has a comparable performance to the ASSA but it has a much lower computational cost.

The discrete multitone modulation (DMT) systems have been widely used in various applications. The DMT system can be considered as a dual of a subband coder, obtained by using the synthesis bank as the transmitter and analysis bank as the receiver. In designing optimal subband coders, the objective is to minimize output quantization noise, whereas in the problem of designing optimal DMT system, the objective function to be minimized is the transmitted power. We show that the design of optimal DMT systems can be formulated as a hypothetical design problem of optimal subband coders. The solution of optimal DMT system can be obtained using existing design methods for optimal biorthogonal subband coders.

The lapped orthogonal transform (LOT) is a popular transform and has found many applications in signal processing. Its extension, the biorthogonal lapped transform (BOLT), has been investigated in detail by Vaidyanathan and Chen (see IEEE Trans. Signal Processing, p.1103-15, 1995). In this paper, we study the lapped unimodular transform (LUT). All of these three transforms are first-order matrices with FIR inverses. We show that like LOT and BOLT, all LUTs can be factorized into degree-one unimodular matrices. The factorization is both minimal and complete. We also show that all first-order systems with FIR inverses can be minimally factorized as a cascade of degree-one LOT, BOLT, and unimodular building blocks. However unlike LOT and BOLT, unimodular filter banks of any order (which include LUTs as a special case) can never have linear phase.

Discrete multitone modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform 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, which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT communication.

Discrete Fourier transform (DFT) based discrete multitone modulation (DMT) systems have been widely applied to various applications. We study a broader class of DMT systems using more general unitary matrices instead of DFT matrices. For this class we show how to design the optimal DMT systems over fading channels with colored noise. Examples are given to show the improvement over the traditional DFT based DMT system. In addition we introduce a modified DFT based DMT system. The new system has the same complexity but better noise rejection property.

A novel minimum noise structure is introduced for ladder-based biorthogonal filter banks. The proposed minimum noise ladder-based biorthogonal (MINLAB) coder ensures that the noise gain of the quantizers is unity, even though the system is not orthonormal. The coding gain of the optimal MINLAB coder is always greater than unity. For both the AR(1) and MA(1) processes, the MINLAB coder with 2 taps outperforms the optimal orthonormal coders of any number of taps. In addition to its superior coding performance, the optimal biorthogonal coder has a very low design and implementational cost. Moreover the proposed coder enjoys many advantages that make it an attractive choice for lossy/lossless data compression.

In this letter, we introduce a novel two-channel biorthogonal subband coder. The new coder employs the ladder structure (or so-called wavelet with lifting scheme). The coding gain of the biorthogonal coder is always greater than or equal to unity, and it can be expressed in closed form. Moreover the proposed coder has a very low complexity and the perfect reconstruction property is structurally preserved. Given any filter order, the optimal solution can be found by the well-known Levinson fast algorithm. For both AR(1) process and MA(1) process, the proposed biorthogonal coder with 2 taps has a higher coding than the optimal orthonormal coder with infinite number of taps.

We introduce a polyphase representation for linear time-varying (LTV) filters. Using the proposed polyphase approach, we are able to show some unusual properties of LTV filter bank (FB) that have not been pointed out before. The problem of interchangeability of analysis and synthesis banks is considered. Lossless TVFBs is studied in detail. Perfect reconstruction (PR) can always be obtained for lossless TVFBs. However, in general a PR lossless TVFB will only generate a tight frame.

If a discrete time signal x(n) is bandlimited appropriately we can decimate it without aliasing. However, there exists a broad class of non bandlimited signals which can be recovered perfectly from their decimated versions. We consider both uniform and nonuniform decimation of this kind and explore some applications, especially in noise shaping and in /spl Sigma/-/spl Delta/ modulator type of architectures.

In this paper, we consider the problem of computation of wavelet functions generated from perfect reconstruction filter banks with rational filters. We derive the dilation equations in recursive form and show how to exploit the recursive equations to compute the limit functions. We also derive a recursive equation for the cascade algorithm introduced by Daubechies. The recursive equations link the limit functions directly to the coefficients of the difference equation instead of impulse responses. In both cases, the proposed recursive method has significant computational saving. Furthermore, all the low sensitivity and efficient structures (such as lattice structure) developed in signal processing can be directly applied for wavelet computation. As an application, we show that the class of IIR orthogonal cardinal scaling functions can be computed exactly at all dyadic rationals by using the recursive equations. Recursive formulas for the 2D quincunx wavelets are also derived.

If a discrete time signal x(n) is obtained as the output of an interpolation filter F(z), it is natural to expect that it can be recovered from the decimated samples x(Mn), even though the signal is not bandlimited except in the ideal case. However, unless F(z) is a Nyquist filter, stability of reconstruction is not guaranteed. There are cases where x(n) cannot be recovered from the uniformly spaced samples x(Mn) in a stable manner, for example, when all the polyphase components of F(z) have unit-circle zeros. We provide precise theorems which show that even under such situations, stable reconstruction from a nonuniformly decimated version is often possible.

A new class of two-channel biorthogonal filter banks is derived. The framework covers two useful subclasses: (i) causal stable IIR filter banks; (ii) linear phase FIR filter banks. Perfect reconstruction is structurally preserved and the structural complexity is very low. Filter banks of high frequency selectivity can be achieved by simply designing a single transfer function. Furthermore zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. We also map the proposed 1D framework into 2D. The mapping preserves: (i) perfect reconstruction; (ii) stability in the IIR case; (iii) linear phase in the FIR case; (iv) zeros at aliasing frequency and (v) frequency characteristic of the filters.>

The Chinese remainder theorem (CRT) [McClellan and Rader 1979] has been well known for applications in fast DFT computations and computer arithmetic. Guessoum and Mersereau [1986] first made headway in extending the CRT to multidimensional (MD) nonseparable systems and showing its usefulness. The present letter generalize the result and present a more general form. This more general MDCRT is an exact counterpart of 1DCRT.>