Cyclic Filter Banks Research Articles

Filter banks on discrete abelian groups

In this work, we provide polyphase, modulation, and frame theoretical analyses of a filter bank on a discrete abelian group. Thus, multi-dimensional or cyclic filter banks as well as filter banks for signals in [Formula: see text] or [Formula: see text] spaces are studied in a unified way. We obtain perfect reconstruction conditions and the corresponding frame bounds in this particular context.

Optimum low complexity filter bank for generalized orthogonal frequency division multiplexing

Generalized frequency division multiplexing (GFDM) is one of the multicarrier modulation candidates proposed for the 5th generation of wireless networks. Among GFDM linear receivers, GFDM MMSE receiver achieves the best error performance for multipath fading channels at the cost of high numerical complexity. Hence, the combination of GFDM match filter (MF) receiver and double-side successive interference cancellation (DSIC) method is used instead. However, there is a significant gap between the error performance of GFDM MMSE and DSIC/MF receivers for the case of employing modern channel coding. Recently, we have proposed a new multicarrier scheme based on GFDM architecture called generalized orthogonal frequency division multiplexing (GOFDM). This study derives an optimized cyclic tree-structured perfect reconstruction-quadrature mirror filter (PR-QMF) bank for GOFDM transceiver and then introduces a novel method for implementation of the optimum filter bank in the frequency domain. Employing such a fast and optimum filter bank provides several advantages for GOFDM transceiver. GOFDM transmitter mitigates out-of-band spectrum leak to the level of that of GFDM. In addition, choosing an appropriate configuration of filter bank yields lower peak to average power ratio in transmit signal of GOFDM compared to that of OFDM. On the other hand, while GOFDM MMSE receiver has lower numerical complexity compared with GFDM DSIC/MF receiver, its coded bit error rate curve is close to that of GFDM MMSE receiver. The aforementioned advantages envision GOFDM as a competitive candidate to be employed in the physical layer of new wireless applications.

Error performance analysis for generalized orthogonal frequency division multiplexing

Generalized Frequency Division Multiplexing (GFDM) is a cyclic filtered multicarrier modulation that may be employed for many new wireless applications. However, due to its non-orthogonal structure, a trade-off between the complexity and error performance should be considered in the design of GFDM receivers. This study proposes an orthogonal cyclic filtered multicarrier modulation called Generalized Orthogonal Frequency Division Multiplexing (GOFDM), which is based on the cyclic Perfect Reconstruction-Quadrature Mirror Filter (PR-QMF) bank. We first derive the frequency domain matrix descriptions for GOFDM linear receivers based on which, the impact of PR-QMF bank on the GOFDM error performance has been theoretically analyzed. Furthermore, the error performance of GOFDM and GFDM linear receivers are compared for AWGN and multipath fading channels. As shown through simulations, GOFDM MMSE receiver outperforms GFDM receiver where the performance gap is significant in case of low-order QAM constellations and multipath fading channels.

Multi-channel filter banks associated with linear canonical transform

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This paper investigates multi-channel filter banks associated with the LCT. First, the perfect reconstruction (PR) conditions are analyzed and design method of PR filter banks for the LCT is proposed, which demonstrates that the LCT based filter banks can inherit conventional design methods of filter banks in the Fourier domain. Then polyphase decompositions in the LCT domain are defined and polyphase realization of the LCT based filter banks is derived in terms of polyphase matrices. Furthermore, multi-channel cyclic filter banks associated with the LCT are proposed by defining circular convolution in the LCT domain. The PR design method and polyphase representation of cyclic filter banks for the LCT are derived similarly. Finally, simulations validate the proposed design methods of the LCT based filter banks and also demonstrate potential application of the LCT based cyclic filter banks in image subband decomposition.

Efficient Block-Based Frequency Domain Wavelet Transform Implementations

Subband decompositions for image coding have been explored extensively over the last few decades. The condensed wavelet packet (CWP) transform is one such decomposition that was recently shown to have coding performance advantages over conventional decompositions. A special feature of the CWP is that its design and implementation are performed in the cyclic frequency domain. While performance gains have been reported, efficient implementations of the CWP (or more generally, efficient implementations of cyclic filter banks) have not yet been fully explored. In this paper, we present efficient block-based implementations of cyclic filter banks along with an analysis of the arithmetic complexity. Block-based cyclic filter bank implementations of the CWP coder are compared with conventional subband/wavelet image coders whose filter banks are implemented in the time domain. It is shown that block-based cyclic filter bank implementations can result in CWP coding systems that outperform the popular image coding systems both in terms of arithmetic complexity and coding performance.

Design method for two-channel cyclic filter banks over fields of characteristic two

A new perfect reconstruction condition for two-channel biorthogonal cyclic filter banks over fields of characteristic two is introduced, from which a technique for designing such filter banks is described. The result is based on a new transform, the cyclic Z-transform over a finite field.

Fractional Fourier domain analysis of cyclic multirate signal processing

The cyclic filter banks, which are used widely in the image subband coding, refer to signal processing on the finite field. This study investigates the fractional Fourier domain (FRFD) analysis of cyclic multirate systems based on the fractional circular convolution and chirp period. The proposed theorems include the fractional Fourier domain analysis of cyclic decimation and cyclic interpolation, the noble identities of cyclic decimation and cyclic interpolation in the FRFD, the polyphase representation of cyclic signal in the FRFD, and the perfect reconstruction condition for the cyclic filter banks in the FRFD. Furthermore, this paper proposes the design methods for perfect reconstruction cyclic filter bank and cyclic filter bank with chirp modulation in the FRFD. The proposed theorems extend the multirate signal processing in the FRFD, which also advance the applications of the theorems of filter bank in the FRFD on the finite signal field, such as digital image processing. At last, the proposed design methods for the cyclic filter banks in the FRFD are validated by simulations.

Design of an Optimal Two-Channel Orthogonal Cyclic Filterbank Using Semidefinite Programming

A simple method for the design of an optimal two-channel orthogonal cyclic filterbank using semidefinite programming is presented. The criterion for optimality is to maximize the passband energy, or equivalently, to minimize the stopband energy of the filter's impulse response. The objective function and orthogonality constraints are represented in terms of the cyclic autocorrelation sequence of the filter's impulse response. The convex formulation of the filter design problem is obtained by imposing the positive semidefinite property on the cyclic autocorrelation matrix. The solution of the semidefinite programming problem gives a class of optimal cyclic filters with unique discrete Fourier transform magnitude response. The design method is illustrated with an example.

A realization method of cyclic filter banks

AbstractIn recent years theories on filter banks (cyclic filter banks) in cyclic LTI systems have been proposed. Not only are cyclic filter banks that use cyclic convolution suitable for processes such as picture signals (finite signals), the design of cyclic filter banks is also limited to specific discrete frequency points. Consequently, there are advantages such as greater freedom of design compared to filter banks (noncyclic filter banks) in noncyclic LTI systems which use conventional linear convolution. Definite design methods have been given which realize a two‐partition construction as a cyclic filter bank with linear phase characteristics and orthogonality at the same time not possible in conventional noncyclic filter banks up to the present. Other than this, there have been no discussions on multipartition construction utilizing, for example, a modulated structure, methods that utilize various other advantages which can obtain a cyclic LTI system, or discussions on problems which can be solved by these. Based on this, we propose one method to achieve a cyclic filter bank in this paper. We propose a configuration that uses DFT modulation. To start with, we lead with polyphase expressions of cyclic filter banks that use DFT modulation and then present complete reconstruction conditions. We subsequently mention that the complete reconstruction conditions are given as a linear equation whose synthesized coefficients are unknown parameters by means of using a resolution given beforehand. Next, we examine the essential properties of a cyclic LTI system and then describe the advantages of this configuration method obtained by means of using these properties. Finally, we provide a design example of the proposed cyclic filter bank and show that a cyclic filter bank can be configured with DFT modulation. In addition, we mention the combined effects when dividing and synthesizing image signals based on applying this method to image compression applications. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(5): 9– 18, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20070

Multirate signal processing on finite fields

The paper addresses the problem of multirate signal processing over arbitrary fields. Studies of multirate systems and filter banks have proceeded in parallel, and a wealth of results are available in literature. The authors concentrate their attention on cyclic systems. These structures are ideally suited to generalising the concepts to finite fields. The perfect reconstruction property for quadrature mirror filter banks is obtained. It is shown how the cyclic wavelet transform (CWT) can be derived from such systems; the relationships between cyclic filter banks and CWTs are explored in detail. The results obtained are potentially very well suited for speech and image encoding, as well as for fast algorithms in signal processing.

Design of two-channel linear phase orthogonal cyclic filterbanks

We propose a method to design an orthonormal two-channel cyclic filterbank (CFB) with real analysis and synthesis filters having linear phase. This is particularly significant, since it is not possible to realize regular two-channel linear phase orthogonal filterbanks (unless the filters are two-tap). The lowpass filter of the FB is obtained as a spectral factor of a zero phase Nyquist(2) filter, which is optimized. We show that the CFB design is computationally less demanding as compared to the noncyclic case, and it may be possible to get better filters. We design the CFB for a particular case and show that this filterbank is not a noncyclic orthogonal filterbank.