An Approach for Synthesis of Modulated -Channel FIR Filter Banks Utilizing the Frequency-Response Masking Technique
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Research Article An Approach for Synthesis of Modulated M-Channel FIR Filter Banks Utilizing the Frequency-Response Masking Technique ´ Rosenbaum, Per Lowenborg, ¨ Linnea and H˚akan Johansson Department of Electrical Engineering, Link¨oping University, 581 83 Link¨oping, Sweden Received 22 December 2005; Revised 29 June 2006; Accepted 26 August 2006 Recommended by Soontorn Oraintara The frequency-response masking (FRM) technique was introduced as a means of generating linear-phase FIR filters with narrow transition band and low arithmetic complexity. This paper proposes an approach for synthesizing modulated maximally decimated FIR filter banks (FBs) utilizing the FRM technique. A new tailored class of FRM filters is introduced and used for synthesizing nonlinear-phase analysis and synthesis filters. Each of the analysis and synthesis FBs is realized with the aid of only three subfilters, one cosine-modulation block, and one sine-modulation block. The overall FB is a near-perfect reconstruction (NPR) FB which in this case means that the distortion function has a linear-phase response but small magnitude errors. Small aliasing errors are also introduced by the FB. However, by allowing these small errors (that can be made arbitrarily small), the arithmetic complexity can be reduced. Compared to conventional cosine-modulated FBs, the proposed ones lower significantly the overall arithmetic complexity at the expense of a slightly increased overall FB delay in applications requiring narrow transition bands. Compared to other proposals that also combine cosine-modulated FBs with the FRM technique, the arithmetic complexity can typically be reduced by 40% in specifications with narrow transition bands. Finally, a general design procedure is given for the proposed FBs and examples are included to illustrate their benefits. Copyright © 2007 Linn´ea Rosenbaum et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Maximally decimated FBs (see Figure 1) find applications in numerous areas [1–3]. Over the past two decades, a vast number of papers on the theory and design of such FBs have been published. Traditionally, the attention has to a large extent been paid to the problem of designing perfect reconstruction (PR) FBs. In a PR FB, the output sequence of the overall system is simply a shifted version of the input sequence. However, FBs are most often used in applications where small errors (emanating from quantizations, etc.) are inevitable and allowed. Imposing PR on the FB is then an unnecessarily severe restriction which may lead to a higher arithmetic complexity than is actually required to meet the specification at hand (arithmetic complexity is defined in this article as the number of arithmetic operations per sample needed in an implementation of an FB). To reduce the complexity one should therefore use near perfect reconstruction (NPR
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