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. © 2008 IEEE.published_or_final_versio

A Generalized Window Approach for Designing Transmultiplexers

This paper proposes a computational, very efficient, approach for designing a novel family of M-channel maximally decimated nearly perfect-reconstruction cosine-modulated transmultiplexers. This approach is referred to as the generalized windowing method for transmultiplexers because after knowing the transmission channel a proper weighted sum of the inter-channel and inter-symbol interferences can be properly taken into account in the optimization of the window function, unlike in other existing windowing techniques. The proposed approach has also the following two advantages. First, independent of the number of subchannels and the common order of the subchannel filters, the number of unknowns is only four. Second, the overall optimization procedure is made considerably fast by estimating the above-mentioned sum in terms of two novel measures, namely, the signal to inter-symbol and the signal to inter-channel interferences, which are very easy to evaluate. Furthermore, when the transmission channel is not considered in the design, a table is provided, which contains the parameters for designing the prototype filter directly by using the windowing method without any time-consuming optimization. When comparing the resulting transmultiplexers with the corresponding perfect-reconstruction designs (the same number of subchannels and same prototype filter order), the levels of interferences are practically the same. However, when the system is affected by a strong narrowband interference, the proposed transmultiplexers outperform their PR counterparts. Design examples are included illustrating the efficiency of the proposed design approach over other existing techniques based on the use of the windowing method

Computation of the para-pseudoinverse for oversampled filter banks: Forward and backward Greville formulas

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Frames and oversampled filter banks have been extensively studied over the past few years due to their increased design freedom and improved error resilience. In frame expansions, the least square signal reconstruction operator is called the dual frame, which can be obtained by choosing the synthesis filter bank as the para-pseudoinverse of the analysis bank. In this paper, we study the computation of the dual frame by exploiting the Greville formula, which was originally derived in 1960 to compute the pseudoinverse of a matrix when a new row is appended. Here, we first develop the backward Greville formula to handle the case of row deletion. Based on the forward Greville formula, we then study the computation of para-pseudoinverse for extended filter banks and Laplacian pyramids. Through the backward Greville formula, we investigate the frame-based error resilient transmission over erasure channels. The necessary and sufficient condition for an oversampled filter bank to be robust to one erasure channel is derived. A postfiltering structure is also presented to implement the para-pseudoinverse when the transform coefficients in one subband are completely lost

Design of multi-plet perfect reconstruction filter banks using frequency-response masking technique

This paper proposes a new design method for a class of two-channel perfect reconstruction (PR) filter banks (FBs) called multi-plet FBs with very sharp cutoff using frequency- response masking (FRM) technique. The multi-plet FBs are PR FBs and their frequency characteristics are controlled by a single subfilter. By recognizing the close relationship between the subfilter and the FRM-based halfband filter, very sharp cutoff PR multi-plet FBs can be realized with reduced implementation complexity. The design procedure is very general and it can be applied to both linear-phase and low-delay PR FBs. Design examples are given to demonstrate the usefulness of the proposed method. © 2008 IEEE.published_or_final_versio

Biorthogonality in lapped transforms : a study in high-quality audio compression

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 76-82).by Shiufun Cheung.Ph.D

On the vectorization of FIR filterbanks

This paper presents a vectorization technique to implement FIR filterbanks. The word vectorization, in the context of this work, refers to a strategy in which all iterative operations are replaced by equivalent vector and matrix operations. This approach allows that the increasing parallelism of the most recent computer processors and systems be properly explored. The vectorization techniques are applied to two kinds of FIR filterbanks (conventional and recursive), and are presented in such a way that they can be easily extended to any kind of FIR filterbanks. The vectorization approach is compared to other kinds of implementation that do not explore the parallelism, and also to a previous FIR filter vectorization approach. The tests were performed in Matlab and C, in order to explore different aspects of the proposed technique

On the design and multiplierless realization of perfect reconstruction triplet-based FIR filter banks and wavelet bases

This paper proposes new methods for the efficient design and realization of perfect reconstruction (PR) two-channel finite-impulse response (FIR) triplet filter banks (FBs) and wavelet bases. It extends the linear-phase FIR triplet FBs of Ansari et al. to include FIR triplet FBs with lower system delay and a prescribed order of K regularity. The design problem using either the minimax error or least-squares criteria is formulated as a semidefinite programming problem, which is a very flexible framework to incorporate linear and convex quadratic constraints. The K regularity conditions are also expressed as a set of linear equality constraints in the variables to be optimized and they are structurally imposed into the design problem by eliminating the redundant variables. The design method is applicable to linear-phase as well as low-delay triplet FBs. Design examples are given to demonstrate the effectiveness of the proposed method. Furthermore, it was found that the analysis and synthesis filters of the triplet FB have a more symmetric frequency responses. This property is exploited to construct a class of PR M-channel uniform FBs and wavelets with M = 2 L, where L is a positive integer, using a particular tree structure. The filter lengths of the two-channel FBs down the tree are approximately reduced by a factor of two at each level or stage, while the transition bandwidths are successively increased by the same factor. Because of the downsampling operations, the frequency responses of the final analysis filters closely resemble those in a uniform FB with identical transition bandwidth. This triplet-based uniform M-channel FB has very low design complexity and the PR condition and K regularity conditions are structurally imposed. Furthermore, it has considerably lower arithmetic complexity and system delay than conventional tree structure using identical FB at all levels. The multiplierless realization of these FBs using sum-of-power-of-two (SOPOT) coefficients and multiplier block is also studied. © 2004 IEEE.published_or_final_versio