Biorthogonal Cosine-modulated Filter Banks Research Articles

Efficient Design of High-Complexity Cosine Modulated Filter Banks Using $2 M$th Band Conditions

This paper presents several new properties of biorthogonal cosine modulated filter banks (CMFBs) and efficient algorithms for designing CMFBs with a very large number of subbands and very long filters. For a biorthogonal CMFB, we find the periodicity and symmetry of its overall transfer function and aliasing transfer functions which can be efficiently computed based on a decimated uniform discrete Fourier transform (DFT) analysis filter bank. By exploiting gradient information and 2M th band conditions, efficient algorithms are proposed for designing both orthogonal and biorthogonal CMFBs. In addition, an efficient matrix inversion algorithm with O(N 2 ) complexity is also presented. Several numerical examples and comparisons with many other existing methods are included to demonstrate the design performance and efficiency of the algorithms.

Efficient Design of Cosine Modulated Filter Banks Based on Gradient Information

An efficient iterative algorithm is first proposed for the design of biorthogonal cosine modulated filter banks (CMFBs) with nearly perfect reconstruction. The design problem is formulated as a quadratic unconstrained least-squares minimization problem, in which the gradient vector of the objective function with respective to unknown parameters can be obtained analytically. The algorithm is then modified for the design of orthogonal CMFBs. Design examples and comparisons are included that show that the proposed design method leads to filter banks with improved performance.

Biorthogonal Recombination Nonuniform Cosine-Modulated Filter Banks and their Multiplier-Less Realizations

This paper studies the theory, design and multiplier-less (ML) realization of a class of perfect reconstruction (PR) low-delay biorthogonal nonuniform cosine-modulated filter banks (CMFBs). It is based on a recombination (or merging) structure previously proposed by the authors. By relaxing the original CMFB and the recombination transmultiplexer (TMUX) in the recombination structure to be biorthogonal, nonuniform CMFBs with lower system delay can be obtained. This also increases the possible choices of the prototype filters to meet different design objectives. A matching condition is introduced to suppress the spurious response resulting from the mismatch in the transition bands of the two biorthogonal CMFBs. A complete factorization of biorthgonal CMFB using the lifting scheme is employed to obtain structurally PR biorthogonal nonuniform filter banks (FBs), which are robust to coefficient quantization. In addition, by approximating the lifting coefficients and the modulation matrices by the sum of powers-of-two (SOPOT) coefficients, ML realization with very low implementation complexity is obtained. Design examples and comparison are given to illustrate the effectiveness of the proposed method.

Efficient biorthogonal cosine-modulated filter banks

Biorthogonal modulated filter banks, when compared to paraunitary ones, provide the advantage that the overall system delay can be chosen independently of the filter length, thus allowing to design low delay filter banks. They have recently been studied by several authors. In this paper, we connect two different design methods, namely the quadratic constrained least-squares optimization and the principle of cascading sparse self-inverse matrices. Moreover, we show how factorizations into zero-delay and maximum-delay matrices can be utilized in order to achieve desirable features such as structure-inherent perfect reconstruction, no DC leakage of the filter bank, and a low implementation cost.