Nonuniform filter banks: a reconstruction and design theory

Nayebi, K.; Barnwell, T.P.; Smith, M.J.T.

doi:10.1109/78.205717

Cited by 91 publications

(51 citation statements)

References 14 publications

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“…This definition includes the so-called block decimation [3], in which the first R 1 samples of each segment of R 2 samples are retained while the rest are discarded. By our notation, the block decimation R 2 : R 1 is represented as ↓ M with…”

Section: Nonuniform Decimation and Decimation Patternsmentioning

confidence: 99%

“…The design has been studied by many researchers [3], [6]- [9], in which the design methods are based on the generalized sampling theorem, assuming that the original signals to be sampled are band-limited below the Nyquist frequency. Then the optimal filter (or the perfect reconstruction filter) is given by an ideal lowpass filter with complex coefficients [2], [8].…”

Section: Introductionmentioning

confidence: 99%

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H∞ Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

Nagahara

Ogura

Yamämoto

2011

SICE Journal of Control, Measurement, and System Integration

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: In this paper, we consider signal interpolation of discrete-time signals which are decimated nonuniformly. A conventional interpolation method is based on the sampling theorem, and the resulting system consists of an ideal filter with complex-valued coefficients. While the conventional method assumes band limitation of signals, we propose a new method by sampled-data H ∞ optimization. By this method, we can remove the band-limiting assumption and the optimal filter can be with real-valued coefficients. Moreover, we show that without band-limited assumption, there can be the optimal decimation patterns among ones with the same ratio. By examples, we show the effectiveness of our method.

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Section: Nonuniform Decimation and Decimation Patternsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

H∞ Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

Nagahara

Ogura

Yamämoto

2011

SICE Journal of Control, Measurement, and System Integration

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“…, the lapped transform is PR [1], [11]. Thus, we can design good near-PR nonuniform lapped transforms by minimizing , e.g., by using unconstrained minimization techniques such as the quasi-Newton method [12].…”

Section: Note That Ifmentioning

confidence: 99%

“…Furthermore, with nonuniform filter banks, low-frequency components are not subject to additional distortion due to window switching. Various methods have been proposed for designing nonuniform filter banks [4]- [11]. Many are based on the subband merging approach [4]- [9], while others are based on a tree-structured design [1], [3] or constructed from joining uniform filter banks by a transition filter [10].…”

Section: Introductionmentioning

confidence: 99%

A practical approach for the design of nonuniform lapped transforms

Yoon

Malvar

2006

IEEE Signal Process. Lett.

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Abstract-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.Index Terms-Cosine-modulated filter banks (CMFBs), extended lapped transforms (ELTs), filter banks, lapped transforms, modulated lapped transform (MLT), nonuniform filter banks.

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“…However, as stated earlier, there are nonuniform PRFBs that cannot be built in this manner. Many works deal with approximate reconstruction (or 'near-PR') nonuniform FBs, e.g., the frequency domain approaches of Li et al [7], the time domain methods of Nayebi et al [8], and other references therein. These are very useful from a practical standpoint, giving FBs with excellent filter responses and low aliasing distortions.…”

Section: Relevant Earlier Workmentioning

confidence: 99%

Nonuniform Filter Banks: New Results and open Problems

Akkarakaran¹,

Vaidyanathan²

2003

Studies in Computational Mathematics

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Abstract. A nonuniform filter bank (FB) is one whose channel decimation rates need not all be equal. While the theory and design of uniform FBs is a very well developed subject, there are several interesting open issues in the area of nonuniform FBs. Most nonuniform FB designs either result in approximate or near-perfect reconstruction, or involve cascading uniform FBs in tree structures. This leaves unanswered many important theoretical issues involved in obtaining perfect reconstruction (PR) in nonuniform FBs. The purpose of this paper is to address these issues. We only study FBs with integer decimation rates, as FBs with rational decimators can also be shown to be transformable to them. The central problem of interest is as follows: Let S be a set of positive integers obeying maximal decimation (i.e., with reciprocals summing to unity). Find necessary and sufficient conditions on S for existence of a PRFB belonging to some FB class C and using S as its set of decimators. The class C is defined by some constraint on the filters of its constituent FBs; examples of interest are the class of all rational FBs (FBs with rational filters), FIR FBs, orthonormal FBs, etc. A condition that immediately suggests itself is the one stating that the integers be arrangeable in a tree so that the required PRFB can be built by cascading uniform PRFBs in a tree structure. However, this condition, while clearly sufficient, is not necessary for many classes C of interest. In fact there are sets violating it which can be used to build delay-chain PRFBs (in which all filters are delays). Many of our new results focus on the class of rational FBs. We strengthen considerably the known necessary conditions in this case, and provide new ones. The basic problem remains unresolved -necessary and sufficient conditions are still unknown, however we believe our work is an important step towards a full solution. We conclude by listing all known conditions, studying their inter-relationship, and pointing out several open problems.

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Nonuniform filter banks: a reconstruction and design theory

Cited by 91 publications

References 14 publications

H∞ Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

H∞ Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

A practical approach for the design of nonuniform lapped transforms

Nonuniform Filter Banks: New Results and open Problems

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Nonuniform filter banks: a reconstruction and design theory

Cited by 91 publications

References 14 publications

H&infin; Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

H&infin; Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

A practical approach for the design of nonuniform lapped transforms

Nonuniform Filter Banks: New Results and open Problems

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H∞ Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

H∞ Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals