摘要 :
This paper offers a new multiple signal restoration tool to solve the inverse problem, when signals are convoluted with a multiple impulse response and then degraded by an additive noise signal with multiple components. Inverse pr...
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This paper offers a new multiple signal restoration tool to solve the inverse problem, when signals are convoluted with a multiple impulse response and then degraded by an additive noise signal with multiple components. Inverse problems arise practically in all areas of science and engineering and refers to as methods of estimating data/parameters, in our case of multiple signals that cannot directly be observed. The presented tool is based on the mapping multiple signals into the quaternion domain, and then solving the inverse problem. Due to the non-commutativity of quaternion arithmetic, it is difficult to find the optimal filter in the frequency domain for degraded quaternion signals. As an alternative, we introduce an optimal filter by using special 4x4 matrices on the discrete Fourier transforms of signal components, at each frequency-point. The optimality of the solution is with respect to the mean-square-root error, as in the classical theory of the signal restoration by the Wiener filter. The Illustrative example of optimal filtration of multiple degraded signals in the quaternion domain is given. The computer simulations validate the effectiveness of the proposed method.
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摘要 :
This paper offers a new multiple signal restoration tool to solve the inverse problem, when signals are convoluted with a multiple impulse response and then degraded by an additive noise signal with multiple components. Inverse pr...
展开
This paper offers a new multiple signal restoration tool to solve the inverse problem, when signals are convoluted with a multiple impulse response and then degraded by an additive noise signal with multiple components. Inverse problems arise practically in all areas of science and engineering and refers to as methods of estimating data/parameters, in our case of multiple signals that cannot directly be observed. The presented tool is based on the mapping multiple signals into the quaternion domain, and then solving the inverse problem. Due to the non-commutativity of quaternion arithmetic, it is difficult to find the optimal filter in the frequency domain for degraded quaternion signals. As an alternative, we introduce an optimal filter by using special 4x4 matrices on the discrete Fourier transforms of signal components, at each frequency-point. The optimality of the solution is with respect to the mean-square-root error, as in the classical theory of the signal restoration by the Wiener filter. The Illustrative example of optimal filtration of multiple degraded signals in the quaternion domain is given. The computer simulations validate the effectiveness of the proposed method.
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摘要 :
We briefly introduce the quaternion linear canonical transform (QLCT), which is a generalization of the quaternion Fourier transform (QFT) to the linear canonical transform (LCT) domain. We show that the QLCT can be reduced to the...
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We briefly introduce the quaternion linear canonical transform (QLCT), which is a generalization of the quaternion Fourier transform (QFT) to the linear canonical transform (LCT) domain. We show that the QLCT can be reduced to the quaternion Fourier transform (QFT). We then derive the inverse transform of the QLCT using the properties of the QFT. We finally provide an example which describes the relationship between the QFT and the QLCT.
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摘要 :
We briefly introduce the quaternion linear canonical transform (QLCT), which is a generalization of the quaternion Fourier transform (QFT) to the linear canonical transform (LCT) domain. We show that the QLCT can be reduced to the...
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We briefly introduce the quaternion linear canonical transform (QLCT), which is a generalization of the quaternion Fourier transform (QFT) to the linear canonical transform (LCT) domain. We show that the QLCT can be reduced to the quaternion Fourier transform (QFT). We then derive the inverse transform of the QLCT using the properties of the QFT. We finally provide an example which describes the relationship between the QFT and the QLCT.
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