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Animesh Kumar - One of the best experts on this subject based on the ideXlab platform.
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Sampling smooth spatio-temporal physical fields: When will the Aliasing Error increase with time?
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: Karthik Sharma, Animesh KumarAbstract:Acquisition of physical fields, such as temperature along a path, using a distributed array of sensors (samples) is of interest. For smooth spatial fields, in a Nyquist style sampling setup, the Aliasing Error is determined by the (spatial) spectral profile of a field. Physical fields and their spectral properties evolve with time. In this work, the spectral evolution of spatio-temporal fields is analyzed, where the field is given by physical law comprising of a constant coefficient linear partial differential equation. A procedure to examine whether field's spatial spectral profile will become worse with time, from Aliasing point of view, is developed. The procedure is exemplified using a second-order PDE in this work. The analysis is extended to include simple point source terms. Techniques such as the Fourier transform, the unilateral Laplace transform, and root-locus plot from control theory are utilized in this work.
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ICASSP - Sampling smooth spatio-temporal physical fields: When will the Aliasing Error increase with time?
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: Karthik Sharma, Animesh KumarAbstract:Acquisition of physical fields, such as temperature along a path, using a distributed array of sensors (samples) is of interest. For smooth spatial fields, in a Nyquist style sampling setup, the Aliasing Error is determined by the (spatial) spectral profile of a field. Physical fields and their spectral properties evolve with time. In this work, the spectral evolution of spatio-temporal fields is analyzed, where the field is given by physical law comprising of a constant coefficient linear partial differential equation. A procedure to examine whether field's spatial spectral profile will become worse with time, from Aliasing point of view, is developed. The procedure is exemplified using a second-order PDE in this work. The analysis is extended to include simple point source terms. Techniques such as the Fourier transform, the unilateral Laplace transform, and root-locus plot from control theory are utilized in this work.
Karthik Sharma - One of the best experts on this subject based on the ideXlab platform.
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Sampling smooth spatio-temporal physical fields: When will the Aliasing Error increase with time?
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: Karthik Sharma, Animesh KumarAbstract:Acquisition of physical fields, such as temperature along a path, using a distributed array of sensors (samples) is of interest. For smooth spatial fields, in a Nyquist style sampling setup, the Aliasing Error is determined by the (spatial) spectral profile of a field. Physical fields and their spectral properties evolve with time. In this work, the spectral evolution of spatio-temporal fields is analyzed, where the field is given by physical law comprising of a constant coefficient linear partial differential equation. A procedure to examine whether field's spatial spectral profile will become worse with time, from Aliasing point of view, is developed. The procedure is exemplified using a second-order PDE in this work. The analysis is extended to include simple point source terms. Techniques such as the Fourier transform, the unilateral Laplace transform, and root-locus plot from control theory are utilized in this work.
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ICASSP - Sampling smooth spatio-temporal physical fields: When will the Aliasing Error increase with time?
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: Karthik Sharma, Animesh KumarAbstract:Acquisition of physical fields, such as temperature along a path, using a distributed array of sensors (samples) is of interest. For smooth spatial fields, in a Nyquist style sampling setup, the Aliasing Error is determined by the (spatial) spectral profile of a field. Physical fields and their spectral properties evolve with time. In this work, the spectral evolution of spatio-temporal fields is analyzed, where the field is given by physical law comprising of a constant coefficient linear partial differential equation. A procedure to examine whether field's spatial spectral profile will become worse with time, from Aliasing point of view, is developed. The procedure is exemplified using a second-order PDE in this work. The analysis is extended to include simple point source terms. Techniques such as the Fourier transform, the unilateral Laplace transform, and root-locus plot from control theory are utilized in this work.
Yoram Bresler - One of the best experts on this subject based on the ideXlab platform.
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upper bounds on Aliasing Error energy for multidimensional sampling of nonbandlimited signals
International Conference on Acoustics Speech and Signal Processing, 2008Co-Authors: Behzad Sharif, Yoram BreslerAbstract:We present upper bounds on the 2-norm of the Aliasing Error in multidimensional Shannon sampling. Our bounds complement the previously known 1-norm upper bounds for the peak Aliasing Error. The proposed bounds provide a good estimate of the total Error energy for any signal, rather than just for certain pathological extremals, as is the case with the 1-norm bounds which, as a result, tend to be too conservative for practical applications. The sampling representation is general, possibly multiband, and not restricted to bandlimited signals. Error bounds are phrased in terms of the energy of signal components that lie outside the assumed band-region. Therefore, they are easy to interpret and compute as is demonstrated for two practical signal classes, namely signals with exponential or polynomial out-of-band decay.
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ICASSP - Upper bounds on Aliasing Error energy for multidimensional sampling of nonbandlimited signals
2008 IEEE International Conference on Acoustics Speech and Signal Processing, 2008Co-Authors: Behzad Sharif, Yoram BreslerAbstract:We present upper bounds on the 2-norm of the Aliasing Error in multidimensional Shannon sampling. Our bounds complement the previously known 1-norm upper bounds for the peak Aliasing Error. The proposed bounds provide a good estimate of the total Error energy for any signal, rather than just for certain pathological extremals, as is the case with the 1-norm bounds which, as a result, tend to be too conservative for practical applications. The sampling representation is general, possibly multiband, and not restricted to bandlimited signals. Error bounds are phrased in terms of the energy of signal components that lie outside the assumed band-region. Therefore, they are easy to interpret and compute as is demonstrated for two practical signal classes, namely signals with exponential or polynomial out-of-band decay.
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perfect reconstruction formulas and bounds on Aliasing Error in sub nyquist nonuniform sampling of multiband signals
IEEE Transactions on Information Theory, 2000Co-Authors: R Venkataramani, Yoram BreslerAbstract:We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class /spl Bscr/(/spl Fscr/) of multiband signals with spectral support /spl Fscr/, at rates arbitrarily close to the Landau (1969) minimum rate equal to the Lebesgue measure of /spl Fscr/, even when /spl Fscr/ does not tile R under translation. Using the conditions for exact reconstruction, we derive an explicit reconstruction formula. We compute bounds on the peak value and the energy of the Aliasing Error in the event that the input signal is band-limited to the "span of /spl Fscr/" (the smallest interval containing /spl Fscr/) which is a bigger class than the valid signals /spl Bscr/(/spl Fscr/), band-limited to /spl Fscr/. We also examine the performance of the reconstruction system when the input contains additive sample noise.
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sub nyquist sampling of multiband signals perfect reconstruction and bounds on Aliasing Error
International Conference on Acoustics Speech and Signal Processing, 1998Co-Authors: R Venkataramani, Yoram BreslerAbstract:We consider the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. We derive the conditions for exact reconstruction and find an explicit reconstruction formula. Key features of this method are that the sampling rate can be made arbitrarily close to the minimum (Landau) rate and that it can handle classes of multiband signals that are not packable. We compute various bounds on the Aliasing Error due to mismodeling the spectral support and examine the performance in the presence of additive white sample noise. Finally we provide optimal designs for the reconstruction system.
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Bounds on the Aliasing Error in multidimensional Shannon sampling
IEEE Transactions on Information Theory, 1996Co-Authors: Yoram BreslerAbstract:We present a pair of sharp lower and upper bounds on the 2-norm of the Aliasing Error in general multiband sampling representations for not necessarily bandlimited multidimensional functions. These bounds improve and generalize previous bounds. They also complement a uniform upper bound due to Higgins (1985).
Zhen Zhang - One of the best experts on this subject based on the ideXlab platform.
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estimation of Aliasing Error in sampling theorem for signals not necessarily in wavelet subspaces
International Conference on Acoustics Speech and Signal Processing, 1993Co-Authors: Xianggen Xia, Zhen ZhangAbstract:Some explicit Error bounds are obtained in terms of a signal and a wavelet basis. An application of the Error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed. From the Error bounds, it is clear that a wavelet basis can be adjusted so that the Aliasing Error can be reduced for a fixed signal. >
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ICASSP (3) - Estimation of Aliasing Error in sampling theorem for signals not necessarily in wavelet subspaces
IEEE International Conference on Acoustics Speech and Signal Processing, 1993Co-Authors: Xianggen Xia, Zhen ZhangAbstract:Some explicit Error bounds are obtained in terms of a signal and a wavelet basis. An application of the Error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed. From the Error bounds, it is clear that a wavelet basis can be adjusted so that the Aliasing Error can be reduced for a fixed signal. >
Xianggen Xia - One of the best experts on this subject based on the ideXlab platform.
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estimation of Aliasing Error in sampling theorem for signals not necessarily in wavelet subspaces
International Conference on Acoustics Speech and Signal Processing, 1993Co-Authors: Xianggen Xia, Zhen ZhangAbstract:Some explicit Error bounds are obtained in terms of a signal and a wavelet basis. An application of the Error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed. From the Error bounds, it is clear that a wavelet basis can be adjusted so that the Aliasing Error can be reduced for a fixed signal. >
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ICASSP (3) - Estimation of Aliasing Error in sampling theorem for signals not necessarily in wavelet subspaces
IEEE International Conference on Acoustics Speech and Signal Processing, 1993Co-Authors: Xianggen Xia, Zhen ZhangAbstract:Some explicit Error bounds are obtained in terms of a signal and a wavelet basis. An application of the Error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed. From the Error bounds, it is clear that a wavelet basis can be adjusted so that the Aliasing Error can be reduced for a fixed signal. >
