The Experts below are selected from a list of 375 Experts worldwide ranked by ideXlab platform
Franz Hlawatsch - One of the best experts on this subject based on the ideXlab platform.
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Frame-theoretic analysis of oversampled filter banks
2013Co-Authors: Helmut Bölcskei, Franz Hlawatsch, Hans G. FeichtingerAbstract:Abstract—We provide a frame-theoretic analysis of oversampled finite impulse response (FIR) and infinite impulse response (IIR) uniform filter banks (FB’s). Our analysis is based on a new relationship between the FB’s Polyphase matrices and the frame operator corresponding to an FB. For a given oversampled analysis FB, we present a parameterization of all synthesis FB’s providing perfect reconstruction. We find necessary and sufficient conditions for an oversampled FB to provide a frame expansion. A new frame-theoretic procedure for the design of paraunitary FB’s from given nonparaunitary FB’s is formulated. We show that the frame bounds of an FB can be obtained by an eigenanalysis of the Polyphase matrices. The relevance of the frame bounds as a characterization of important numerical properties of an FB is assessed by means of a stochastic sensitivity analysis. We consider special cases in which the calculation of the frame bounds and synthesis filters is simplified. Finally, simulation results are presented. Index Terms — Filter banks, frames, oversampling, Polyphase Representation
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Discrete Zak transforms, Polyphase transforms, and applications
IEEE Transactions on Signal Processing, 1997Co-Authors: Helmut Bölcskei, Franz HlawatschAbstract:We consider three different versions of the Zak (1967) transform (ZT) for discrete-time signals, namely, the discrete-time ZT, the Polyphase transform, and a cyclic discrete ZT. In particular, we show that the extension of the discrete-time ZT to the complex z-plane results in the Polyphase transform, an important and well-known concept in multirate signal processing and filter bank theory. We discuss fundamental properties, relations, and transform pairs of the three discrete ZT versions, and we summarize applications of these transforms. In particular, the discrete-time ZT and the cyclic discrete ZT are important for discrete-time Gabor (1946) expansion (Weyl-Heisenberg frame) theory since they diagonalize the Weyl-Heisenberg frame operator for critical sampling and integer oversampling. The Polyphase Representation plays a fundamental role in the theory of filter banks, especially DFT filter banks. Simulation results are presented to demonstrate the application of the discrete ZT to the efficient calculation of dual Gabor windows, tight Gabor windows, and frame bounds.
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Discrete Zak transforms, Polyphase transforms, and applications
1997Co-Authors: Helmut Bölcskei, Student Member, Franz HlawatschAbstract:Abstract — We consider three different versions of the Zak transform (ZT) for discrete-time signals, namely, the discretetime ZT, the Polyphase transform, and a cyclic discrete ZT. In particular, we show that the extension of the discrete-time ZT to the complex �-plane results in the Polyphase transform, an important and well-known concept in multirate signal processing and filter bank theory. We discuss fundamental properties, relations, and transform pairs of the three discrete ZT versions, and we summarize applications of these transforms. In particular, the discrete-time ZT and the cyclic discrete ZT are important for discrete-time Gabor expansion (Weyl–Heisenberg frame) theory since they diagonalize the Weyl–Heisenberg frame operator for critical sampling and integer oversampling. The Polyphase Representation plays a fundamental role in the theory of filter banks, especiall
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Equivalence Of Dft Filter Banks And Gabor Expansions
1995Co-Authors: Helmut Bölcskei, Franz Hlawatsch, Hans G. FeichtingerAbstract:Recently connections between the wavelet transform and filter banks have been established. We show that similar relations exist between the Gabor expansion and DFT filter banks. We introduce the "z-Zak transform" by suitably extending the discrete-time Zak transform and show its equivalence to the Polyphase Representation. A systematic discussion of parallels between DFT filter banks and Weyl-Heisenberg frames (Gabor expansion theory) is then given. Among other results, it is shown that tight Weyl-Heisenberg frames correspond to paraunitary DFT filter banks. 1 INTRODUCTION AND OUTLINE The wavelet transform, filter banks, and multiresolution signal analysis have recently been unified within a single theory. 1--6 This led to new results and deeper insights in both areas. In this paper, we show that an important linear time-frequency Representation known as the Gabor expansion 7--9 and the computationally efficient DFT filter banks 10--14,6 can be unified in a similar manner. 15 ..
Edoardo Mosca - One of the best experts on this subject based on the ideXlab platform.
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Special low-order IIR filter bank design
2005 13th European Signal Processing Conference, 2005Co-Authors: Zhisheng Duan, Cishen Zhang, Jingxin Zhang, Edoardo MoscaAbstract:The model matching problem minR(z)∥W(z)-R(z)E(z)∥ involved in multirate filter banks design is addressed. A method is presented to design the synthesis filter bank R(z) with the order of W(z) which is the Polyphase Representation of the time delay of the reconstructed signal. The existence conditions of such low-order R(z) are given in linear matrix inequalities (LMIs). The corresponding H2 model matching problem is solved in the same fashion. The results are illustrated through examples. Examples demonstrate the possibility of improving signal reconstruction error and reducing the order of synthesis filters simultaneously by increasing moderately time delay.
Helmut Bölcskei - One of the best experts on this subject based on the ideXlab platform.
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Frame-theoretic analysis of oversampled filter banks
2013Co-Authors: Helmut Bölcskei, Franz Hlawatsch, Hans G. FeichtingerAbstract:Abstract—We provide a frame-theoretic analysis of oversampled finite impulse response (FIR) and infinite impulse response (IIR) uniform filter banks (FB’s). Our analysis is based on a new relationship between the FB’s Polyphase matrices and the frame operator corresponding to an FB. For a given oversampled analysis FB, we present a parameterization of all synthesis FB’s providing perfect reconstruction. We find necessary and sufficient conditions for an oversampled FB to provide a frame expansion. A new frame-theoretic procedure for the design of paraunitary FB’s from given nonparaunitary FB’s is formulated. We show that the frame bounds of an FB can be obtained by an eigenanalysis of the Polyphase matrices. The relevance of the frame bounds as a characterization of important numerical properties of an FB is assessed by means of a stochastic sensitivity analysis. We consider special cases in which the calculation of the frame bounds and synthesis filters is simplified. Finally, simulation results are presented. Index Terms — Filter banks, frames, oversampling, Polyphase Representation
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Discrete Zak transforms, Polyphase transforms, and applications
IEEE Transactions on Signal Processing, 1997Co-Authors: Helmut Bölcskei, Franz HlawatschAbstract:We consider three different versions of the Zak (1967) transform (ZT) for discrete-time signals, namely, the discrete-time ZT, the Polyphase transform, and a cyclic discrete ZT. In particular, we show that the extension of the discrete-time ZT to the complex z-plane results in the Polyphase transform, an important and well-known concept in multirate signal processing and filter bank theory. We discuss fundamental properties, relations, and transform pairs of the three discrete ZT versions, and we summarize applications of these transforms. In particular, the discrete-time ZT and the cyclic discrete ZT are important for discrete-time Gabor (1946) expansion (Weyl-Heisenberg frame) theory since they diagonalize the Weyl-Heisenberg frame operator for critical sampling and integer oversampling. The Polyphase Representation plays a fundamental role in the theory of filter banks, especially DFT filter banks. Simulation results are presented to demonstrate the application of the discrete ZT to the efficient calculation of dual Gabor windows, tight Gabor windows, and frame bounds.
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Discrete Zak transforms, Polyphase transforms, and applications
1997Co-Authors: Helmut Bölcskei, Student Member, Franz HlawatschAbstract:Abstract — We consider three different versions of the Zak transform (ZT) for discrete-time signals, namely, the discretetime ZT, the Polyphase transform, and a cyclic discrete ZT. In particular, we show that the extension of the discrete-time ZT to the complex �-plane results in the Polyphase transform, an important and well-known concept in multirate signal processing and filter bank theory. We discuss fundamental properties, relations, and transform pairs of the three discrete ZT versions, and we summarize applications of these transforms. In particular, the discrete-time ZT and the cyclic discrete ZT are important for discrete-time Gabor expansion (Weyl–Heisenberg frame) theory since they diagonalize the Weyl–Heisenberg frame operator for critical sampling and integer oversampling. The Polyphase Representation plays a fundamental role in the theory of filter banks, especiall
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Equivalence Of Dft Filter Banks And Gabor Expansions
1995Co-Authors: Helmut Bölcskei, Franz Hlawatsch, Hans G. FeichtingerAbstract:Recently connections between the wavelet transform and filter banks have been established. We show that similar relations exist between the Gabor expansion and DFT filter banks. We introduce the "z-Zak transform" by suitably extending the discrete-time Zak transform and show its equivalence to the Polyphase Representation. A systematic discussion of parallels between DFT filter banks and Weyl-Heisenberg frames (Gabor expansion theory) is then given. Among other results, it is shown that tight Weyl-Heisenberg frames correspond to paraunitary DFT filter banks. 1 INTRODUCTION AND OUTLINE The wavelet transform, filter banks, and multiresolution signal analysis have recently been unified within a single theory. 1--6 This led to new results and deeper insights in both areas. In this paper, we show that an important linear time-frequency Representation known as the Gabor expansion 7--9 and the computationally efficient DFT filter banks 10--14,6 can be unified in a similar manner. 15 ..
Jos B T M Roerdink - One of the best experts on this subject based on the ideXlab platform.
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Polyphase decompositions and shift invariant discrete wavelet transforms in the frequency domain
Signal Processing, 2010Co-Authors: Alle Meije Wink, Jos B T M RoerdinkAbstract:Given a signal and its Fourier transform, we derive formulas for its Polyphase decomposition in the frequency domain and for the reconstruction from the Polyphase Representation back to the Fourier Representation. We present two frequency-domain implementations of the shift-invariant periodic discrete wavelet transform (SI-DWT) and its inverse: one that is based on frequency-domain Polyphase decomposition and a more efficient 'direct' implementation, based on a reorganisation of the a trous algorithm. We analyse the computational complexities of both algorithms, and compare them to existing time-domain and frequency domain implementations of the SI-DWT. We experimentally demonstrate the reduction in computation time achieved by the direct frequency domain implementation of the SI-DWT for wavelet filters with non-compact support.
Jingxin Zhang - One of the best experts on this subject based on the ideXlab platform.
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techniques for constructing biorthogonal bipartite graph filter banks
IEEE Transactions on Signal Processing, 2015Co-Authors: D B H Tay, Jingxin ZhangAbstract:The processing of data defined on irregular discrete domains, i.e., graph signals, is becoming an emerging area with great application potential. Using spectral graph theory, Narang and Ortega (2013) laid the framework for two channel filter banks with critical sampling for bipartite graph signals. The bipartite graph filter bank can be extended to any arbitrary graph using the notion of separable filtering. The design of the biorthogonal filter banks by Narang and Ortega (2013) is based on the factorization of a maximally flat polynomial. The factorization technique does not allow much control of the spectral response of the graph filters, resulting in response asymmetry. In this paper, we present a generic framework for constructing biorthogonal graph filter banks that does not require factorization. We introduce the notion of Polyphase Representation and ladder structures for graph filter banks. We show that filters having virtual spectral symmetry and almost energy preservation can be constructed without any sophisticated optimization. Fine control of the spectral response can also be achieved with ease.
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Special low-order IIR filter bank design
2005 13th European Signal Processing Conference, 2005Co-Authors: Zhisheng Duan, Cishen Zhang, Jingxin Zhang, Edoardo MoscaAbstract:The model matching problem minR(z)∥W(z)-R(z)E(z)∥ involved in multirate filter banks design is addressed. A method is presented to design the synthesis filter bank R(z) with the order of W(z) which is the Polyphase Representation of the time delay of the reconstructed signal. The existence conditions of such low-order R(z) are given in linear matrix inequalities (LMIs). The corresponding H2 model matching problem is solved in the same fashion. The results are illustrated through examples. Examples demonstrate the possibility of improving signal reconstruction error and reducing the order of synthesis filters simultaneously by increasing moderately time delay.