A practical approach for the design of nonuniform lapped transforms

We propose a simple method for the design of lapped transforms with nonuniform frequency resolution and good time localization. The method is a generalization of an approach previously proposed by Princen, where the nonuniform filter bank is obtained by joining uniform cosine-modulated filter banks (CMFBs) using a transition filter. We use several transition filters to obtain a near perfect-reconstruction (PR) nonuniform lapped transform with significantly reduced overall distortion. The main advantage of the proposed method is in reducing the length of the transition filters, which leads to a reduction in processing delay that can be useful for applications such as real-time audio coding

Finite-channel chromatic derivative filter banks

Two previous contributions discussed the theory of perfect-reconstruction (PR) chromatic derivative filter banks comprising an infinite number of channels. This paper extends the theory to the case of finite channels. A novel time domain procedure is delineated for designing the synthesis filters that achieve PR in this case

Bidimensional PR QMF with FIR Filters

Multidimensional perfect reconstruction (PR) quadrature mirror filter (QMF) banks with finite impulse response (FIR) filters induced from systems of biorthogonal multivariate scaling functions and wavelets are investigated. In particular, bivariate scaling functions and wavelets with dilation as an expansive integer matrix whose determinant is two in absolute value are considered. Demonstrative quincunxial examples are explicitly given and new FIR filters are constructed

The design of a class of perfect reconstruction two-channel FIR linear-phase filterbanks and wavelets bases using semidefinite programming

This paper proposes a new method for designing a class of two-channel perfect reconstruction (PR) linear-phase FIR filterbanks (FBs) and wavelets previously proposed by Phoong et al. By expressing the given K-regularity constraints as a set of linear equality constraints in the design variables, the design problem using the minimax error criterion can be solved using semidefinite programming (SDP). Design examples show that the proposed method is very effective and it yields equiripple stopband response while satisfying the given K-regularity condition.published_or_final_versio

Theory and design of a class of M-channel IIR cosine-modulated filter banks

This letter proposes a method for designing a class of M-channel, causal, stable, perfect reconstruction (PR) IIR cosine-modulated filter banks (CMFB). The proposed CMFB has the same denominator for all its polyphase components in the prototype filter. Therefore, the PR condition is considerably simplified, and it is relatively simple to satisfy the PR and the casual-stable requirements of the IIR CMFB. Design examples show that the proposed IIR CMFB has sharper cutoff, higher stopband attenuation, and passband flatness than its FIR counterparts, especially when the system delay is small.published_or_final_versio

New design method for two-channel perfect reconstruction IIR filter banks

In this paper, a new method for designing perfect reconstruction (PR) two-channel causal stable IIR filter banks is introduced. It is based on a structure previously proposed by Phoong et al. [2]. By using a combination of allpass and linear-phase FIR functions, the bumping problem found in the conventional structural PR filter bank is significantly suppressed. The design problem is formulated as a polynomial approximation problem and is solved effectively using the Remez exchange algorithm. Filter banks with flexible stopband attenuation and system delay can readily be obtained using the proposed algorithm.published_or_final_versio

Efficient method for designing two-channel PR FIR filter banks with low system delay

In this paper, an efficient method for designing perfect reconstruction (PR) two-channel finite impulse response (FIR) filter banks with low system delay is proposed. It is based on the use of nonlinear-phase FIR function in a structure previously proposed by Phoong et al. The design problem is formulated as a complex polynomial approximation problem and is solved effectively using the Remez exchange algorithm with very low design complexity. Design examples show that filter banks with flexible stopband attenuation and system delay can be readily obtained by the proposed algorithm.published_or_final_versio

Theory and design of arbitrary-length biorthogonal cosine-modulated filter banks

IEEE International Symposium on Circuits and Systems, Hong Kong, China, 9-12 June 1997The design and generalization of Perfect-reconstruction (PR) cosine-modulated filter banks (CMFB) have been studied extensively due to its low design and implementation complexity. In this paper, the theory and design of arbitrary-length biorthogonal CMFB is considered. This is a generalization of the method used in [5] for designing arbitrary length orthogonal CMFB and has the advantage of simple design procedure. We also propose a systematic design method so that biorthogonal CMFB with longer length can be obtained.published_or_final_versio

Role of anticausal inverses in multirate filter-banks. II. The FIR case, factorizations, and biorthogonal lapped transforms

For pt. I see ibid., vol.43, no.5, p.1090, 1990. In part I we studied the system-theoretic properties of discrete time transfer matrices in the context of inversion, and classified them according to the types of inverses they had. In particular, we outlined the role of causal FIR matrices with anticausal FIR inverses (abbreviated cafacafi) in the characterization of FIR perfect reconstruction (PR) filter banks. Essentially all FIR PR filter banks can be characterized by causal FIR polyphase matrices having anticausal FIR inverses. In this paper, we introduce the most general degree-one cafacafi building block, and consider the problem of factorizing cafacafi systems into these building blocks. Factorizability conditions are developed. A special class of cafacafi systems called the biorthogonal lapped transform (BOLT) is developed, and shown to be factorizable. This is a generalization of the well-known lapped orthogonal transform (LOT). Examples of unfactorizable cafacafi systems are also demonstrated. Finally it is shown that any causal FIR matrix with FIR inverse can be written as a product of a factorizable cafacafi system and a unimodular matrix

Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems

We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with oversampling factors of at least two, we provide prescriptions for the shortest filter length of the synthesis bank that would guarantee PR almost surely. The prescribed length is as short or shorter than the analysis filters and has an approximate inverse relationship with the oversampling factor. Our results are in form of necessary and sufficient statements that hold generically, hence only fail for elaborately-designed nongeneric examples. We provide extensive numerical verification of the theoretical results and demonstrate that the gap between the derived filter length prescriptions and the true minimum is small. The results have potential applications in synthesis FB design problems, where the analysis bank is given, and for analysis of fundamental limitations in blind signals reconstruction from data collected by unknown subsampled multi-channel systems.Comment: Manuscript submitted to IEEE Transactions on Signal Processin