Perfect-reconstruction Cosine-modulated Filter Banks Research Articles

A Novel Design of Sparse Prototype Filter for Nearly Perfect Reconstruction Cosine-Modulated Filter Banks

Cosine-modulated filter banks play a major role in digital signal processing. Sparse FIR filter banks have lower implementation complexity than full filter banks, while keeping a good performance level. This paper presents a fast design paradigm for sparse nearly perfect-reconstruction (NPR) cosine-modulated filter banks. First, an approximation function is introduced to reduce the non-convex quadratically constrained optimization problem to a linearly constrained optimization problem. Then, the desired sparse linear phase FIR prototype filter is derived through the orthogonal matching pursuit (OMP) performed under the weighted l 2 norm. The simulation results demonstrate that the proposed scheme is an effective paradigm to design sparse NPR cosine-modulated filter banks.

Design perfect reconstruction cosine-modulated filter banks via quadratically constrained quadratic programming and least squares optimization

In this paper, the design of perfect reconstruction (PR) cosine-modulated filter banks (CMFBs) is implemented via quadratically constrained quadratic programming (QCQP) and least squares (LS) optimization. To this end, a PR CMFB design problem is formulated as a nonconvex QCQP after re-arranging the coefficients of the prototype filter. Then a deep insight is offered into the algebraic relationship between the PR conditions and near-perfect reconstruction (NPR) ones for CMFB designs. Here we theoretically show that the NPR conditions are just the summations of the PR conditions. Firmly in the light of this relationship, a two-stage method is proposed for PR CMFB design. We firstly solve an NPR CMFB problem to obtain its optimal solution as a reference point, then model the PR CMFB design problem as a series of small-sized LS problems near the reference point. And we solve the LS problems in parallel with cheap iteration. Our analysis and numerical results show that the proposed method bears superior performance on effectiveness and efficiency, especially in the case of designing PR CMFBs with large number of channels.

Design perfect reconstruction cosine-modulated filter bank by variable neighbourhood search-least-mean-square error

In multirate digital signal processing, cosine-modulated filter banks (CMFB) satisfying perfect reconstruction (PR) or near-perfect reconstruction (NPR) property are of great interest owing to their extensive applications in data compression, feature detection and extraction and signal transmultiplexing. And the key to PR CMFB design is to design a PR prototype filter (PF). However, designing optimal PR and NPR PF is essentially a constrained non-linear programming. It is generally modelled as a non-convex quadratically constrained quadratic optimisation problem. So far, this kind of optimisation is still a very difficult class of optimisation and no practical but few metaheuristic algorithm is availabe for finding its global optimal solution. The study proposed a two-stage method for designing PR PF. In the first stage, a metaheuristic algorithm based on variable neighbourhood search is proposed for designing lower-ordered PR PF, that is the corresponding PR CMFB has less channels. Then a least-mean-square error approach is introduced to increase the length of the designed lower-ordered PF with the PR property unchanged. Design examples are given to illustrate the proposed algorithm outperforms the existing one in reconstruction error and stopband attenuation.

Implementation of Linear-Phase FIR Nearly Perfect Reconstruction Cosine-Modulated Filterbanks Utilizing the Coefficient Symmetry

The analysis and synthesis parts of a cosine-modulated M-channel filterbank (FB) contain two sections, a modulation block and a prototype filter implemented in a polyphase structure. Although, in many cases, a linear-phase prototype filter is used, the coefficient symmetry of this filter is not utilized when using the existing polyphase structure. In this paper, a method is proposed for implementing a linear-phase prototype filter building a nearly perfect reconstruction cosine-modulated FB in such a way that it enables one to partially utilize the coefficient symmetry, thereby reducing the number of required multiplications in the implementation. The proposed method can be applied for implementing FBs with an arbitrary filter order and number of channels. Moreover, it is shown that, in all cases under consideration, the cosine-modulation part of the FB can be implemented by using a fast discrete cosine transform. The efficiency of the proposed implementation is evaluated by means of examples.

On the Design of Nearly-PR and PR FIR Cosine Modulated Filter Banks Having Approximate Cosine-Rolloff Transition Band

This paper proposes an efficient method for designing nearly perfect reconstruction (NPR) and perfect reconstruction (PR) cosine modulated filter banks (CMFBs) with prototype filters having an approximate cosine-rolloff (CR) transition band. It is shown that the flatness condition required for an NPR CMFB can be automatically satisfied by using a prototype filter with a CR transition band. The design problem is then formulated as a convex minimax optimization problem, and it can be solved by second-order cone programming (SOCP). By using the NPR CMFB so obtained as an initial guess to nonlinear optimizers such as Fmincon in Matlab, high-quality PR CMFBs can be obtained. The advantages of the proposed method are that it does not require a user-supplied initial guess of the prototype filter and bumps in the passband of the analysis filters can be effectively suppressed.

Efficient Implementation of Complex Modulated Filter Banks Using Cosine and Sine Modulated Filter Banks

The recently introduced exponentially modulated filter bank (EMFB) is a -channel uniform, orthogonal, critically sampled, and frequency-selective complex modulated filter bank that satisfies the perfect reconstruction (PR) property if the prototype filter of an -channel PR cosine modulated filter bank (CMFB) is used. The purpose of this paper is to present various implementation structures for the EMFBs in a unified framework. The key idea is to use cosine and sine modulated filter banks as building blocks and, therefore, polyphase, lattice, and extended lapped transform (ELT) type of implementation solutions are studied. The ELT-based EMFBs are observed to be very competitive with the existing modified discrete Fourier transform filter banks (MDFT-FBs) when comparing the number of multiplications/additions and the structural simplicity. In addition, EMFB provides an alternative channel stacking arrangement that could be more natural in certain subband processing applications and data transmission systems.

On the design of high-complexity cosine-modulated transmultiplexers based on the frequency-response masking approach

Two efficient techniques exploiting the frequency-response masking (FRM) approach are proposed in order to make it feasible to design prototype filters for highly selective nearly perfect-reconstruction cosine-modulated transmultiplexers and filter banks (CMTs and CMFBs) having a very large number of channels. In these design schemes, the number of unknowns is drastically reduced when compared with the corresponding techniques for designing direct-form prototype filters. Furthermore, in the proposed techniques, the main figures of merits, that is, the intersymbol interference and the interchannel interference for CMTs and the overall and aliasing distortions for CMFBs are taken into account in a controlled manner. In order to speed up the convergence of these two optimization techniques, simplifications for computing the resulting nonlinear constraints and the corresponding gradient vectors are proposed. They differ from each other in the sense that the first and second ones utilize the frequency-domain and time-domain constraints for controlling the figures of merit, respectively. Combining these two techniques results in numerically efficient algorithms for designing optimized CMTs (or CMFBs) with a reduced computational complexity (number of arithmetic operations per output sample), particularly when both branches of the FRM structure are required. Design examples are included illustrating the efficiency of the design methods and the high performance of the resulting CMT structures.

Performance analysis and prototype filter design for perfect-reconstruction cosine-modulated filter banks with fixed-point implementation

Cosine modulated filter banks have gained popularity for their ability to provide perfect reconstruction (PR) while maintaining an efficient design and implementation. However, this effectiveness is hindered if the filter bank is implemented in the fixed-point domain where quantization, rounding, and overflow occur, and result in reconstruction errors. In this article we demonstrate how to maintain PR of the filter bank when implementing it in fixed-point number format with constant wordlength. We explore how the frequency selectivity of the analysis and synthesis filters changes from the floating point ones due to fixed-point errors and present new design criteria for filter banks that will be implemented in fixed-point number format.

Power Line Communication Experiment using Wavelet OFDM in U.S..

Recently, the demand of high speed network in home is increasing, and PLC is expected as one of the solutions. We can see related researches on the high speed PLC system using a frequency band 2 MHz to 30 MHz. In this paper, we propose a wavelet based OFDM as a suitable method for realizing the high speed PLC system. The proposed wavelet OFDM method is composed of the M-band transmultiplexer which consists of the perfect reconstruction cosine-modulated filter bank. And the attenuation of the first side-lobe is above 35dB, which is a characteristic of the proposed method. As a result, we show that the proposed method has the inter-carrier interference characteristic which is superior to FFT-OFDM, and it also provides the flexible notch filter function which can reduce the influence on other communication systems existing in the communication band which the PLC uses. Finally, we describe that the simulation results about the BER characteristic of the proposed method in AWGN were almost the same as the theory, and that transmission rates which were measured by using prototype modems in a field test house in U.S. were above 35Mbps.

A low computational complexity algorithm for ECG signal compression

In this work, a filter bank-based algorithm for electrocardiogram (ECG) signals compression is proposed. The new coder consists of three different stages. In the first one—the subband decomposition stage—we compare the performance of a nearly perfect reconstruction (N-PR) cosine-modulated filter bank with the wavelet packet (WP) technique. Both schemes use the same coding algorithm, thus permitting an effective comparison. The target of the comparison is the quality of the reconstructed signal, which must remain within predetermined accuracy limits. We employ the most widely used quality criterion for the compressed ECG: the percentage root-mean-square difference (PRD). It is complemented by means of the maximum amplitude error (MAX). The tests have been done for the 12 principal cardiac leads, and the amount of compression is evaluated by means of the mean number of bits per sample (MBPS) and the compression ratio (CR). The implementation cost for both the filter bank and the WP technique has also been studied. The results show that the N-PR cosine-modulated filter bank method outperforms the WP technique in both quality and efficiency.

Design of practically perfect-reconstruction cosine-modulated filter banks: a second-order cone programming approach

Designing optimal perfect-reconstruction (PR) and near PR (NPR) cosine-modulated filter banks is essentially a constrained nonlinear minimization problem. This paper proposes two second-order cone-programming based algorithms for designing NPR and practically PR cosine-modulated filter banks with improved performance relative to several established design methods.

Frequency Sampling Design of Prototype Filters for Nearly Perfect Reconstruction Cosine-Modulated Filter Banks

A new approach to the design of prototype filters for conventional nearly perfect reconstruction (N-PR) cosine-modulated filter banks is presented. The new method is based on the frequency sampling approach for the design of finite-impulse response filters. In the proposed approach, the magnitude response values of samples in the transition band of the prototype filter are the only parameters to be optimized. The analytical and simulation results show that despite there being no direct control over the stopband attenuation of the prototype filter, the performance of the filter bank is extremely good, and in several cases, the whole system closely satisfies the PR property.

The fast DCT-IV/DST-IV computation via the MDCT

The discrete cosine transform of type IV (DCT-IV) and corresponding discrete sine transform of type IV (DST-IV) have played key role in the efficient implementation of orthogonal lapped transforms and perfect reconstruction cosine-modulated filter banks such as the oddly stacked modified discrete cosine transform (MDCT) or equivalently, the modulated lapped transform (MLT). However, the DCT-IV and DST-IV of double sizes are related to two variants of filter banks defined by Dolby Labs AC-3 digital audio compression algorithm. Since these two variants of filter banks are efficiently computed by recently proposed new fast algorithm for the oddly stacked MDCT (Signal Processing 82 (2002) 433), it is shown that the efficient DCT-IV and DST-IV computation can be realized via the MDCT of double size. The careful analysis of regular structure of the new fast MDCT algorithm allows to extract a new DCT-IV/DST-IV computational structure and to suggest a new sparse matrix factorization of the DCT-IV matrix. Finally, the new DCT-IV/DST-IV computational structure provides an alternative efficient implementation of the forward and inverse MDCT in layer III of MPEG (MP3) audio coding.

Current state and future directions of multirate filter banks and their applications

This paper provides an overview of the basic concepts, current state and future directions of uniform and nonuniform multirate filter banks and their applications. Research in the areas of multidimensional filter banks, and wavelet transforms, as a direct extension to the topic is still proceeding at a rapid rate. Different design techniques and algorithms that are currently of interest are investigated from hardware complexity and reconstructed signals' quality points of view. Important similarities and differences between different filters categories are noted, which lead to a discussion of important issues that need to be resolved. Distortions and quantization effects present in the filter banks are reviewed and some solutions for controlling different types of distortions are introduced. The problem of designing QMF banks that can provide good frequency resolution while allowing for exact or near perfect reconstruction of the signal is quite challenging, because so many dissimilar types of distortion must be minimized and/or eliminated in the same design context. Recently, the perfect reconstruction cosine-modulated filter bank and filter banks with block sampling have emerged as an attractive choice of filter bank with respect to implementation complexities and design cost. New trends and future directions including selective multirate filter banks, filter banks with nonuniform decimation ratio, filter banks with discrete coefficients, multidimensional filter banks, nonlinear filter banks and data dependent decompositions are presented. Finally, some selected applications of multirate filter banks are described; namely transmultiplexers, speech and image coding, analog voice privacy systems and wavelets based signal and image compression.

Optimization of Perfect Reconstruction Cosine-Modulated Filter Banks: Fast Algorithm

Optimization of Perfect Reconstruction Cosine-Modulated Filter Banks: Fast Algorithm

Perceptual coding of digital audio

During the last decade, CD-quality digital audio has essentially replaced analog audio. Emerging digital audio applications for network, wireless, and multimedia computing systems face a series of constraints such as reduced channel bandwidth, limited storage capacity, and low cost. These new applications have created a demand for high-quality digital audio delivery at low bit rates. In response to this need, considerable research has been devoted to the development of algorithms for perceptually transparent coding of high-fidelity (CD-quality) digital audio. As a result, many algorithms have been proposed, and several have now become international and/or commercial product standards. This paper reviews algorithms for perceptually transparent coding of CD-quality digital audio, including both research and standardization activities. This paper is organized as follows. First, psychoacoustic principles are described, with the MPEG psychoacoustic signal analysis model 1 discussed in some detail. Next, filter bank design issues and algorithms are addressed, with a particular emphasis placed on the modified discrete cosine transform, a perfect reconstruction cosine-modulated filter bank that has become of central importance in perceptual audio coding. Then, we review methodologies that achieve perceptually transparent coding of FM- and CD-quality audio signals, including algorithms that manipulate transform components, subband signal decompositions, sinusoidal signal components, and linear prediction parameters, as well as hybrid algorithms that make use of more than one signal model. These discussions concentrate on architectures and applications of those techniques that utilize psychoacoustic models to exploit efficiently masking characteristics of the human receiver. Several algorithms that have become international and/or commercial standards receive in-depth treatment, including the ISO/IEC MPEG family (-1, -2, -4), the Lucent Technologies PAC/EPAC/MPAC, the Dolby AC-2/AC-3, and the Sony ATRAC/SDDS algorithms. Then, we describe subjective evaluation methodologies in some detail, including the ITU-R BS.1116 recommendation on subjective measurements of small impairments. This paper concludes with a discussion of future research directions.

Cosine-modulated filterbanks based on extended Gaussian functions

A new family of cosine-modulated filterbanks based on functions called extended Gaussian functions (EGFs) is obtained. The design is particularly simple since it is mainly based on a closed-form expression. Nearly perfect reconstruction cosine-modulated filterbanks are obtained as well as guidelines to estimate the filterbank parameters. This analytical design method can be used to produce, with a controlled accuracy, filterbanks with practically no upper limitations in the number of coefficients and subbands. Furthermore, a slight modification of the prototype filter coefficients is sufficient to satisfy exactly the perfect reconstruction constraints. An analysis of the time-frequency localization of the discrete prototype filters also shows that under certain conditions, EGF prototypes are at less than 0.3% from the optimal upper bound.

Oversampled cosine modulated filter banks with perfect reconstruction

Oversampled filter banks (FBs) offer more design freedom and better noise immunity than critically sampled FBs. Due to the increased computational complexity caused by oversampling, oversampled FBs allowing an efficient implementation, such as cosine modulated filter banks (CMFBs), are of particular interest. So far, only critically sampled CMFBs have been considered. In this paper, we introduce oversampled CMFBs with perfect reconstruction (PR). Extending a classification of CMFBs recently proposed by Gopinath, we consider two types of oversampled CMFBs with PR. One of these types allows linear phase filters in all channels, and comprises CMFBs recently introduced by Lin and Vaidyanathan as well as Wilson-type CMFBs. For both types of oversampled CMFBs, we formulate PR conditions in the time, frequency, and polyphase domains. It is shown that any PR CMFB corresponds to a PR DFT FB with twice the oversampling factor and that (under a specific condition) the same PR prototype can be used for both CMFB types. We also show that the frame-theoretic properties of a CMFB and of the corresponding DFT FB are closely related. In particular, it is demonstrated that the minimum-norm synthesis prototype in an oversampled PR CMFB equals that in the corresponding DFT FB. Finally, we briefly address design methods and the efficient DCT/DST-based implementation of oversampled CMFBs.

On a novel critically-sampled discrete-time real Gabor transform

In the generalized discrete-time Gabor transform (DTGT), localization of both the dual sequences is not possible at critical sampling. A novel DTGT is defined for real signals and real symmetric synthesis and analysis sequences. It allows small length dual sequences even at critical sampling. The novel DTGT is similar to a modulated lapped transform or a perfect reconstruction cosine-modulated filter bank structure. The novel DTGT is derived and a method to compute the analysis (synthesis) sequence given the synthesis (analysis) sequence is presented. We computed the dual sequences for various popular windows to demonstrate that they have finite lengths, or can be well-approximated by sequences of finite length. We validated the dual sequences by reconstructing a sequence of normally distributed random numbers and demonstrating low mean-square-error in reconstruction. Based on the results, we make some recommendations on the choice of analysis window or filter.

The theory and design of arbitrary-length cosine-modulated filter banks and wavelets, satisfying perfect reconstruction

It is well known that FIR filter banks that satisfy the perfect-reconstruction (PR) property can be obtained by cosine modulation of a linear-phase prototype filter of length N=2mM, where M is the number of channels. In this paper, we present a PR cosine-modulated filter bank where the length of the prototype filter is arbitrary. The design is formulated as a quadratic-constrained least-squares optimization problem, where the optimized parameters are the prototype filter coefficients. Additional regularity conditions are imposed on the filter bank to obtain the cosine-modulated orthonormal bases of compactly supported wavelets. Design examples are given.