The Experts below are selected from a list of 225 Experts worldwide ranked by ideXlab platform
S. Qian - One of the best experts on this subject based on the ideXlab platform.
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Convergence of an iterative time-variant filtering based on discrete Gabor transform
IEEE Transactions on Signal Processing, 1999Co-Authors: S. QianAbstract:An iterative time-variant filtering based on the discrete Gabor transform (DGT) has been previously proposed by the authors. In this article, we present a proof of the convergence of the iterative algorithm under a sufficient condition on the analysis and Synthesis Window functions of the DGT. In the meantime, we show that the iterative algorithm refines the least squares solution.
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Optimal biorthogonal analysis Window function for discrete Gabor transform
IEEE Transactions on Signal Processing, 1994Co-Authors: S. Qian, D. ChenAbstract:Like the DFT/spl minus/a discrete version of the Fourier transform/spl minus/the recently developed discrete Gabor transform (DGT) provides a feasible vehicle to implement the very useful Gabor expansion. In general, the choice of the biorthogonal Window function /spl gamma/(i) is not unique. The authors discuss the solution of /spl gamma/(i) that is optimally close to an arbitrary desired function d(i) when the Synthesis Window h(i) and sampling pattern are given. For d(i)=h(i), the resulting /spl gamma//sub opt/(i) directly leads to so-called orthogonal-like DGT. Combining the DGT, they believe that the result presented in this paper is rather significant for digital signal processing.
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Discrete Gabor transform
IEEE Transactions on Signal Processing, 1993Co-Authors: S. Qian, D. ChenAbstract:A feasible algorithm for implementing the Gabor expansion, the coefficients of which are computed by the discrete Gabor transform (DGT), is presented. For a given Synthesis Window and sampling pattern, computing the auxiliary biorthogonal function of the DGT is nothing more than solving a linear system. The DGT presented applies for both finite as well as infinite sequences. By exploiting the nonuniqueness of the auxiliary biorthogonal function at oversampling an orthogonal like DGT is obtained. As the discrete Fourier transform (DFT) is a discrete realization of the continuous-time Fourier transform, similarly, the DGT introduced provides a feasible vehicle to implement the useful Gabor expansion.
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Optimal biorthogonal functions for finite discrete-time Gabor expansion
Signal Processing, 1992Co-Authors: S. Qian, Kan Chen, Shidong LiAbstract:Abstract One main topic of the Gabor expansion is the selection of the analysis Window and its corresponding biorthogonal Synthesis Window, which in most applications are both required to be concentrated in the joint time and frequency domain. In this paper, we develop an algorithm for computing optimally concentrated biorthogonal functions for the finite discrete-time Gabor expansion. The merit of this approach is demonstrated via numerical simulations.
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A general solution of biorthogonal analysis Window functions for orthogonal-like discrete Gabor transform
[1992] Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 1992Co-Authors: S. Qian, D. ChenAbstract:An algorithm for computing the analysis Window function gamma (i) for the discrete Gabor transform (DGT) corresponding to an arbitrary Synthesis Window function h(i) and sampling pattern is presented. Numerical simulations indicate that the algorithm successfully addresses problems that could not be solved previously due to rank deficiency or numerical instability.
Masahiro Serizawa - One of the best experts on this subject based on the ideXlab platform.
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A family of 3GPP-standard noise suppressors for the AMR codec and the evaluation results
2003 IEEE International Conference on Acoustics Speech and Signal Processing 2003. Proceedings. (ICASSP '03)., 2003Co-Authors: M. Kato, A. Sugiyama, Masahiro SerizawaAbstract:The paper presents a family of 3GPP-standard noise suppressors and the evaluation results. The family consists of a high-quality version and a low-complexity version. These noise suppressors are based on the MMSE STSA (minimum mean square error short time spectral amplitude) algorithm originally proposed by Y. Ephraim and D. Malah (see IEEE Trans. Acoust., Speech, Sig. Processing, vol.ASSP-32, no.6, p.1109-21, 1984). To meet the 3GPP requirements with better speech quality, weighted noise estimation, Synthesis Windowing, and pseudo noise injection are incorporated. Weighted noise estimation enables continuous noise estimation even in the speech period by using weighted noisy speech. The weight is controlled such that a higher estimated SNR gives a smaller weight. A Synthesis Window function is applied between inverse transform and overlap-add processing for smooth transition at frame boundaries. Pseudo noise injection, which is not available in the low-complexity version, modifies the spectral gain based on its nonlinearity. The whole family satisfies all the 3GPP requirements. Results of a full set of evaluations specified by 3GPP are presented for the high-quality version.
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ICASSP (1) - A family of 3GPP-standard noise suppressors for the AMR codec and the evaluation results
2003 IEEE International Conference on Acoustics Speech and Signal Processing 2003. Proceedings. (ICASSP '03)., 2003Co-Authors: M. Kato, A. Sugiyama, Masahiro SerizawaAbstract:The paper presents a family of 3GPP-standard noise suppressors and the evaluation results. The family consists of a high-quality version and a low-complexity version. These noise suppressors are based on the MMSE STSA (minimum mean square error short time spectral amplitude) algorithm originally proposed by Y. Ephraim and D. Malah (see IEEE Trans. Acoust., Speech, Sig. Processing, vol.ASSP-32, no.6, p.1109-21, 1984). To meet the 3GPP requirements with better speech quality, weighted noise estimation, Synthesis Windowing, and pseudo noise injection are incorporated. Weighted noise estimation enables continuous noise estimation even in the speech period by using weighted noisy speech. The weight is controlled such that a higher estimated SNR gives a smaller weight. A Synthesis Window function is applied between inverse transform and overlap-add processing for smooth transition at frame boundaries. Pseudo noise injection, which is not available in the low-complexity version, modifies the spectral gain based on its nonlinearity. The whole family satisfies all the 3GPP requirements. Results of a full set of evaluations specified by 3GPP are presented for the high-quality version.
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Noise suppression with Synthesis Windowing and pseudo noise injection
2002 IEEE International Conference on Acoustics Speech and Signal Processing, 2002Co-Authors: Akihiko Sugiyam, Masanori Kalo, Masahiro SerizawaAbstract:A noise suppression algorithm with Synthesis Windowing and pseudo noise injection is proposed. A Synthesis Window function is applied between inverse transform and overlap-add processing for smooth transition at frame boundaries. The pseudo noise injection modifies the spectral gain based on its nonlinearity. It is selectively disabled for stationary noise so that possible distortion is minimized. Evaluations including subjective assessment show that annoyable peaks of the background noise are suppressed by as much as 15 dB, resulting in a better MOS than that by the EVRC noise suppressor.
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ICASSP - Noise suppression with Synthesis Windowing and pseudo noise injection
IEEE International Conference on Acoustics Speech and Signal Processing, 2002Co-Authors: Akihiko Sugiyam, Masanori Kalo, Masahiro SerizawaAbstract:A noise suppression algorithm with Synthesis Windowing and pseudo noise injection is proposed. A Synthesis Window function is applied between inverse transform and overlap-add processing for smooth transition at frame boundaries. The pseudo noise injection modifies the spectral gain based on its nonlinearity. It is selectively disabled for stationary noise so that possible distortion is minimized. Evaluations including subjective assessment show that annoyable peaks of the background noise are suppressed by as much as 15 dB, resulting in a better MOS than that by the EVRC noise suppressor.
D. Chen - One of the best experts on this subject based on the ideXlab platform.
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Optimal biorthogonal analysis Window function for discrete Gabor transform
IEEE Transactions on Signal Processing, 1994Co-Authors: S. Qian, D. ChenAbstract:Like the DFT/spl minus/a discrete version of the Fourier transform/spl minus/the recently developed discrete Gabor transform (DGT) provides a feasible vehicle to implement the very useful Gabor expansion. In general, the choice of the biorthogonal Window function /spl gamma/(i) is not unique. The authors discuss the solution of /spl gamma/(i) that is optimally close to an arbitrary desired function d(i) when the Synthesis Window h(i) and sampling pattern are given. For d(i)=h(i), the resulting /spl gamma//sub opt/(i) directly leads to so-called orthogonal-like DGT. Combining the DGT, they believe that the result presented in this paper is rather significant for digital signal processing.
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Discrete Gabor transform
IEEE Transactions on Signal Processing, 1993Co-Authors: S. Qian, D. ChenAbstract:A feasible algorithm for implementing the Gabor expansion, the coefficients of which are computed by the discrete Gabor transform (DGT), is presented. For a given Synthesis Window and sampling pattern, computing the auxiliary biorthogonal function of the DGT is nothing more than solving a linear system. The DGT presented applies for both finite as well as infinite sequences. By exploiting the nonuniqueness of the auxiliary biorthogonal function at oversampling an orthogonal like DGT is obtained. As the discrete Fourier transform (DFT) is a discrete realization of the continuous-time Fourier transform, similarly, the DGT introduced provides a feasible vehicle to implement the useful Gabor expansion.
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A general solution of biorthogonal analysis Window functions for orthogonal-like discrete Gabor transform
[1992] Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 1992Co-Authors: S. Qian, D. ChenAbstract:An algorithm for computing the analysis Window function gamma (i) for the discrete Gabor transform (DGT) corresponding to an arbitrary Synthesis Window function h(i) and sampling pattern is presented. Numerical simulations indicate that the algorithm successfully addresses problems that could not be solved previously due to rank deficiency or numerical instability.
Hon Keung Kwan - One of the best experts on this subject based on the ideXlab platform.
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Novel DCT-Based Real-Valued Discrete Gabor Transform and Its Fast Algorithms
IEEE Transactions on Signal Processing, 2009Co-Authors: Hon Keung KwanAbstract:The oversampled Gabor transform is more effective than the critically sampled one in many applications. The biorthogonality relationship between the analysis Window and the Synthesis Window of the Gabor transform represents the completeness condition. However, the traditional discrete cosine transform (DCT)-based real-valued discrete Gabor transform (RGDT) is available only in the critically sampled case and its biorthogonality relationship for the transform has not been unveiled. To bridge these important gaps, this paper proposes a novel DCT-based RDGT, which can be applied in both the critically sampled case and the oversampled case, and their biorthogonality relationships can be derived. The proposed DCT-based RDGT involves only real operations and can utilize fast DCT algorithms for computation, which facilitates computation and implementation by hardware or software as compared to that of the traditional complex-valued discrete Gabor transform. This paper also develops block time-recursive algorithms for the efficient and fast computation of the RDGT and its inverse transform. Unified parallel lattice structures for the implementation of these algorithms are presented. Computational complexity analysis and comparisons have shown that the proposed algorithms provide a more efficient and faster approach for discrete Gabor transforms as compared to those of the existing discrete Gabor transform algorithms. In addition, an application in the noise reduction of the nuclear magnetic resonance free induction decay signals is presented to show the efficiency of the proposed RDGT for time-frequency analysis.
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Novel DCT-based real-valued discrete Gabor transform
2008 IEEE International Symposium on Circuits and Systems, 2008Co-Authors: Hon Keung KwanAbstract:The traditional DCT-based real-valued discrete Gabor transform (RGDT) was limited to the critical sampling case. The biorthogonality relationship between the analysis Window and the Synthesis Window for the transform has not been unveiled. To overcome those drawbacks, this paper proposes a novel DCT-based real-valued discrete Gabor transform, which can be applied under both the critical sampling condition and the over-sampling condition. And the biorthogonality relationship between the analysis Window and the Synthesis Window for the transform is also proved in this paper. Because it only involves real operations and can utilize fast DCT and DDCT algorithms for fast computation, it facilitates computation and implementation by hardware and/or software compared to the traditional complex-valued discrete Gabor transform.
Mj Martin Bastiaans - One of the best experts on this subject based on the ideXlab platform.
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Gabor's signal expansion based on a non-orthogonal sampling geometry
2020Co-Authors: Mj Martin BastiaansAbstract:Gabor’s signal expansion and the Gabor transform are formulated on a nonorthogonal time-frequency lattice instead of on the traditional rectangular lattice. The reason for doing so is that a non-orthogonal sampling geometry might be better adapted to the form of the Window functions (in the time-frequency domain) than an orthogonal one: the set of shifted and modulated versions of the usual Gaussian Synthesis Window, for instance, corresponding to circular contour lines in the time-frequency domain, can be arranged more tightly in a hexagonal geometry than in a rectangular one. Oversampling in the Gabor scheme, which is required to have mathematically more attractive properties for the analysis Window, then leads to better results in combination with less oversampling. The procedure presented in this paper is based on considering the non-orthogonal lattice as a sub-lattice of a denser orthogonal lattice that is oversampled by a rational factor. In doing so, Gabor’s signal expansion on a non-orthogonal lattice can be related to the expansion on an orthogonal lattice (restricting ourselves, of course, to only those sampling points that are part of the non-orthogonal sub-lattice), and all the techniques that have been derived for rectangular sampling – including an optical means of generating Gabor’s expansion coefficients via the Zak transform in the case of integer oversampling – can be used, albeit in a slightly modified form.
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On the non-orthogonal sampling scheme for Gabor's signal expansion
2020Co-Authors: Mj Martin Bastiaans, Van Aj Arno LeestAbstract:Gabor's signal expansion and the Gabor transform are formulated on a non-orthogonal time-frequency lattice instead of on the traditional rectangular lattice [1,2]. The reason for doing so is that a non-orthogonal sampling geometry might be better adapted to the form of the Window functions (in the time-frequency domain) than an orthogonal one: the set of shifted and modulated versions of the usual Gaussian Synthesis Window, for instance, corresponding to circular contour lines in the time-frequency domain, can be arranged more tightly in a hexagonal geometry than in a rectangular one. Oversampling in the Gabor scheme, which is required to have mathematically more attractive properties for the analysis Window, then leads to better results in combination with less oversampling. The new procedure presented in this paper is based on considering the non-orthogonal lattice as a sub-lattice of a denser orthogonal lattice that is oversampled by a rational factor. In doing so, Gabor's signal expansion on a non-orthogonal lattice can be related to the expansion on an orthogonal lattice (restricting ourselves, of course, to only those sampling points that are part of the non-orthogonal sub-lattice), and all the techniques that have been derived for rectangular sampling [1,2] can be used, albeit in a slightly modified form.
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EUSIPCO - Optimum oversampling in the rectangular Gabor scheme
1998Co-Authors: Mj Martin BastiaansAbstract:The Windowed Fourier transform of a time signal is considered, as well as a way to reconstruct the signal from a sufficiently densely sampled version of its Windowed Fourier transform using a Gabor representation; following Gabor, sampling occurs on a two-dimensional time-frequency lattice with equidistant time intervals and equidistant frequency intervals. For sufficiently dense sampling, the Synthesis Window (which appears in Gabor's reconstruction formula) may be constructed such that it resembles a rather arbitrarily given function; this function may or may not be proportional to the analysis Window (which is used in the Windowed Fourier transform). It is shown that the resemblance can already be reached for a rather small degree of over-sampling, if the sampling distances in the time and frequency directions are properly chosen. A procedure is presented with which the optimum ratio of the sampling intervals can be determined.
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On the discrete version of Gabor's signal expansion, the Gabor transform, and the Zak transform
1996Co-Authors: Mj Martin Bastiaans, J.p. VeenAbstract:Gabors expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or Synthesis Window is introduced, along with the inverse operation, i.e., the Gabor transform, which uses an analysis Window that is related to the Synthesis Window and with the help of which Gabors expansion coefficients can be determined. The restriction to a signal and an analysis Window that both have finite-support, leads to the concept of a discrete Gabor expansion and a discrete Gabor transform. After introduction of the discrete Fourier transform and the discrete Zak transform, it is possible to express the discrete Gabor expansion and the discrete Gabor transform as matrix-vector products. Using these matrix-vector products, a relationship between the analysis Window and the Synthesis Window is derived. It is shown how this relationship enables us to determine the optimum Synthesis Window in the sense that it has minimum L_2 norm, and it is shown that this optimum Synthesis Window resembles best the analysis Window.
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Discrete Gabor transform and discrete Zak transform
1996Co-Authors: Mj Martin Bastiaans, N.m. Namazi, K. MatthewsAbstract:Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or Synthesis Window is introduced, along with the inverse operation, i.e. the Gabor transform, which uses an analysis Window that is related to the Synthesis Window and with the help of which Gabor's expansion coefficients can be determined. The restriction to a signal and an analysis Window that both have finite-support, leads to the concept of a discrete Gabor expansion and a discrete Gabor transform. After introduction of the discrete Fourier transform and the discrete Zak transform, it is possible to express the discrete Gabor expansion and the discrete Gabor transform as matrix-vector products. Using these matrix-vector products, a relationship between the analysis Window and the Synthesis Window is derived. It is shown how this relationship enables us to determine the optimum Synthesis Window in the sense that it has minimum L2 norm, and it is shown that this optimum Synthesis Window resembles best the analysis Window.
