Abstract
The recently introduced exponentially modulated filter bank (EMFB) is a -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 -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 ELT-based 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.
Highlights
In many practical applications, the signals under consideration are real-valued
More frequency-selective filter banks can be obtained by using longer and smoother prototype filters. It has been shown in [6,7,8] that highly frequency-selective perfect reconstruction (PR) cosine modulated filter bank (CMFB) can be designed if the order of the prototype filter is N = 2KM − 1 and the overlapping factor K is sufficiently large. (The use of other order selections does not significantly improve the stopband attenuation of the prototype filter as observed in [9, 10].) the critically sampled PR complex modulated filter bank system is possible only if certain additional modifications are introduced for the subband
This paper extends our previous work in [14] by providing more detailed derivation of extended lapped transform (ELT) and polyphase sine modulated filter banks (SMFBs) structures, introducing our lattice structures for SMFBs, presenting an alternative approach to obtain an SMFB using original ELT structures, and comparing the arithmetic complexity of the ELT-based exponentially modulated filter bank (EMFB) with the complexity of MDFT-FBs
Summary
The signals under consideration are real-valued. in communications signal processing, complex-valued in-phase/quadrature (I/Q) signals are commonly used. 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 They provide the PR property if the real-valued FIR linear-phase lowpass prototype filter of an M-channel PR CMFB is used. (The use of other order selections does not significantly improve the stopband attenuation of the prototype filter as observed in [9, 10].) the critically sampled PR complex modulated filter bank system is possible only if certain additional modifications are introduced for the subband. The MCLT is a 2x oversampled system for the processing of real-valued signals, whereas the EMFB is a critically sampled complex modulated filter bank that suits complex-valued signals.
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