To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals, a novel kind of anti-aliasing algorithm based on the short time Fourier transform （STFT） is brought forward. ...To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals, a novel kind of anti-aliasing algorithm based on the short time Fourier transform （STFT） is brought forward. First the physical essence of aliasing that occurs is analyzed; second the interpolation algorithm model is setup based on the Hamming window; then the fast implementation of the algorithm using the Newton iteration method is given. Using the numerical simulation the feasibility of algorithm is validated. Finally, the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.展开更多
Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform （QFT） over ZN based on the elementary transforms, such as Hadamar...Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform （QFT） over ZN based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z_N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z_N. According to probability amplitude, we prove that the transform can be used to realize QFT over ZN and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z_N.展开更多
We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are ...We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are widely used in image compression but their lossy nature exclude them as viable candidates for Kolmogorov Complexity approximations. For the first time, we present a way to adapt fourier transforms for lossless image compression. The proposed method has a very strong Pearsons correlation to existing complexity metrics and we further establish its consistency as a complexity metric by confirming its measurements never exceed the complexity of nothingness and randomness (representing the lower and upper limits of complexity). Surprisingly, many of the other methods tested fail this simple sanity check. A final symmetry-based test also demonstrates our method’s superiority over existing lossless compression metrics. All complexity metrics tested, as well as the code used to generate and augment the original dataset, can be found in our github repository: ECA complexity metrics<sup>1</sup>.展开更多
基金the National Natural Science Foundation of China (90407007 60372001).
文摘To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals, a novel kind of anti-aliasing algorithm based on the short time Fourier transform （STFT） is brought forward. First the physical essence of aliasing that occurs is analyzed; second the interpolation algorithm model is setup based on the Hamming window; then the fast implementation of the algorithm using the Newton iteration method is given. Using the numerical simulation the feasibility of algorithm is validated. Finally, the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.
基金Project supported by the National Basic Research Program of China (Grant No.2013CB338002)
文摘Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform （QFT） over ZN based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z_N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z_N. According to probability amplitude, we prove that the transform can be used to realize QFT over ZN and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z_N.
文摘We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are widely used in image compression but their lossy nature exclude them as viable candidates for Kolmogorov Complexity approximations. For the first time, we present a way to adapt fourier transforms for lossless image compression. The proposed method has a very strong Pearsons correlation to existing complexity metrics and we further establish its consistency as a complexity metric by confirming its measurements never exceed the complexity of nothingness and randomness (representing the lower and upper limits of complexity). Surprisingly, many of the other methods tested fail this simple sanity check. A final symmetry-based test also demonstrates our method’s superiority over existing lossless compression metrics. All complexity metrics tested, as well as the code used to generate and augment the original dataset, can be found in our github repository: ECA complexity metrics<sup>1</sup>.
