Efficient Implementation of Complex Modulated Filter Banks Using Cosine and Sine Modulated Filter Banks
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Efficient Implementation of Complex Modulated Filter Banks Using Cosine and Sine Modulated Filter Banks Ari Viholainen, Juuso Alhava, and Markku Renfors Institute of Communications Engineering, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland Received 12 April 2005; Revised 6 October 2005; Accepted 17 October 2005 Recommended for Publication by Ulrich Heute The recently introduced exponentially modulated filter bank (EMFB) is a 2M-channel uniform, orthogonal, critically sampled, and frequency-selective complex modulated filter bank that satisfies the perfect reconstruction (PR) property if the prototype filter of an M-channel PR cosine modulated filter bank (CMFB) is used. The purpose of this paper is to present various implementation structures for the EMFBs in a unified framework. The key idea is to use cosine and sine modulated filter banks as building blocks and, therefore, polyphase, lattice, and extended lapped transform (ELT) type of implementation solutions are studied. The ELTbased EMFBs are observed to be very competitive with the existing modified discrete Fourier transform filter banks (MDFT-FBs) when comparing the number of multiplications/additions and the structural simplicity. In addition, EMFB provides an alternative channel stacking arrangement that could be more natural in certain subband processing applications and data transmission systems. Copyright © 2006 Ari Viholainen 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
In many practical applications, the signals under consideration are real-valued. However, in communications signal processing, complex-valued in-phase/quadrature (I/Q) signals are commonly used. I/Q signals are obtained in a natural way when the baseband equivalent of a (modulated) bandpass signal is used in analysis or actual signal processing tasks. Another approach is to build an artificial complex-valued signal from two independent real-valued signals by mapping them into real and imaginary parts, respectively [1]. Complex modulated filter banks are widely used as computationally efficient and versatile building blocks whenever subband processing or transmission of complex-valued signals is needed. However, certain applications related to audio/video processing and adaptive filtering can also utilize complex modulated filter banks even if input signals are realvalued [2, 3]. In this way, main aliasing terms are missing and both magnitude and phase information is available. The desired filter bank properties depend highly on the application under consideration. The emphasis of this paper is on 2M-channel finite impulse response (FIR) complex modulated filter banks that are orthogonal, critically sampled, and frequency selective. Moreover, they provide the PR property if the real-valued FIR linear-phase lowpass
prototype filter of an M-channel PR CMFB is used. Due to th
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