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sliding Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform: Fast algorithm and Applications

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2012年第6期59卷 1321-1334页

作者： Wu, Jiasong Wang, Lu Yang, Guanyu Senhadji, Lotfi Luo, Limin Shu, Huazhong Southeast Univ Lab Image Sci & Technol Sch Engn & Comp Sci Nanjing 210096 Jiangsu Peoples R China Ctr Rech Informat Biomed Sino Francais CRIBs Nanjing 210096 Jiangsu Peoples R China INSERM U1099 F-35000 Rennes France Univ Rennes 1 LTSI F-35000 Rennes France Ctr Rech Informat Biomed Sino Francais CRIBs F-35000 Rennes France

This paper presents a fast algorithm for the computation of sliding conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT). The algorithm calculates the values of window i + N/4 from those of window, one length-N/4 Walsh Hadamard transform (WHT) and one length-N/4 Modified WHT (MWHT). The proposed algorithm requires O(N) arithmetic operations, which is more efficient than the block-based algorithms of various transforms and the sliding FFT algorithm, but less efficient than the sliding WHT algorithms. Compared to the recently proposed sliding inverse SCHT (ISCHT) algorithm, the proposed algorithm is more efficient for real input but less efficient for complex input. The applications of the sliding CS-SCHT in transform domain adaptive filtering (TDAF) to complex signal channel equalization and real speech signal acoustic echo cancellation are also provided.

关键词： Conjugate symmetric sequency-ordered complex Hadamard transform fast algorithm sliding algorithm

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Fast Gray Code Kernel algorithm for the sliding Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform

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IEEE ACCESS 2018年 6卷 56029-56045页

作者： Wu, Jiasong Wu, Fuzhi Dong, Zhifang Song, Kaiwen Kong, Youyong Senhadji, Lotfi Shu, Huazhong Southeast Univ Lab Image Sci & Technol Key Lab Comp Network & Informat Integrat Minist Educ Nanjing 210096 Jiangsu Peoples R China Southeast Univ Int Joint Res Lab Informat Display & Visualizat Minist Educ Nanjing 210096 Jiangsu Peoples R China Ctr Rech Informat Biomed Sinofrancais Nanjing 210096 Jiangsu Peoples R China Southeast Univ Sch Elect Sci & Engn Nanjing 210096 Jiangsu Peoples R China INSERM U1099 F-35000 Rennes France Univ Rennes 1 Lab Traitement Signal & Image F-35000 Rennes France Ctr Rech Informat Biomed Sinofrancais F-35000 Rennes France

A fast algorithm based on the gray code kernel (GCK) for computing the conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) in a sliding window is presented. The proposed algorithm computes the current projection value from the previously computed ones. In order to obtain the peculiar computation order of the projection values, we construct the CS-SCHT matrix tree and also introduce the alpha-related concept. The properties of the elements of the CS-SCHT matrix are also given for deriving the GCK sliding CS-SCHT algorithm. The proposed algorithm only needs N/2+log(2)N - 2 (or log(2)N - 1) multiplications with j and 4N - 2 (or 2N - 1) real additions for complex (or real) input data, which is more efficient than the block-based CS-SCHT and other existing sliding complex transform algorithms, such as the radix-4 sliding CS-SCHT algorithm, sliding FFT algorithm, and sliding DFT algorithm. A comparison of the proposed algorithm with other sliding transforms in terms of computation time is also presented to validate the theoretical results.

关键词： Fast algorithm conjugate symmetric sequency-ordered complex Hadamard transform gray code kernel sliding algorithm

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Fast algorithms for the computation of sliding discrete Hartley transforms

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2007年第6期55卷 2937-2944页

作者： Kober, Vitaly CICESE Div Appl Phys Dept Comp Sci Ensenada 22860 Baja California Mexico

Fast algorithms for computing generalized discrete Hartley transforms in a sliding window are proposed. The algorithms are based on second-order recursive relations between subsequent local transform spectra. New efficient inverse algorithms for signal processing in a sliding window are also presented. The computational complexity of the algorithms is compared with that of known fast discrete Hartley transforms and running recursive algorithms.

关键词： discrete Hartley transform (DHT) running algorithm sliding algorithm

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Fast algorithms for the computation of sliding discrete sinusoidal transforms

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2004年第6期52卷 1704-1710页

作者： Kober, V CICESE Div Appl Phys Dept Comp Sci Ensenada 22860 Baja California Mexico

Fast algorithms for computing various discrete cosine transforms and discrete sine transforms in a sliding window are proposed. The algorithms are based on a recursive relationship between three subsequent local transform spectra. Efficient inverse algorithms for signal processing in a sliding window are also presented. The computational complexity of the algorithms is compared with that of known fast discrete sinusoidal transforms and running recursive algorithms.

关键词： discrete cosine transform discrete sine transform running algorithm sliding algorithm

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Recursive algorithms for Computing sliding DCT With Arbitrary Step

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IEEE SENSORS JOURNAL 2021年第10期21卷 11507-11513页

作者： Kober, Vitaly Ctr Sci Res & Higher Educ Ensenada CICESE Dept Comp Sci Ensenada 22860 Baja California Mexico Chelyabinsk State Univ Dept Math Chelyabinsk 454001 Russia Russian Acad Sci RAS Inst Informat Transmiss Problems Moscow 127051 Russia

Discrete cosine transform (DCT) is one of the most popular transforms in digital signal processing. Its close approximation to the Karhunen-Loeve transform implies a high degree of energy compaction. Therefore, it can be used in a wide range of applications such as sensor noise removal, spectral analysis, linear filtering, feature extraction and pattern recognition. When it is required to estimate the spectrum of a nonstationary process such as radar, speech, biomedical and communication signals, a short-time (sliding) transform can be used. Basically, the sliding transform means that the transform is calculated on a fixed-length window of the signal, which is constantly updated with new samples while the oldest ones are discarded. In some engineering applications, when the spectral content changes slowly, the window can slide more than one sample at a time to speed up the spectral analysis. In this paper, second-order recursive algorithms are proposed for fast computing the DCT in windows that are located at a given equal distance from each other. The computational complexity of the algorithms is compared with that of common fast and sliding DCT algorithms.

关键词： Discrete cosine transform sensor noise removal signal processing short-time transform spectrogram sliding algorithm

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Fast algorithms for the Computation of sliding Sequency-Ordered Complex Hadamard Transform

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第11期58卷 5901-5909页

作者： Wu, Jiasong Shu, Huazhong Wang, Lu Senhadji, Lotfi Southeast Univ Lab Image Sci & Technol Sch Biol Sci & Med Engn Nanjing 210096 Peoples R China CRIBs Nanjing 210096 Peoples R China INSERM U 642 F-35000 Rennes France Univ Rennes 1 LTSI F-35000 Rennes France Southeast Univ Lab Image Sci & Technol Sch Comp Sci & Engn Nanjing 210096 Peoples R China

Fast algorithms for computing the forward and inverse sequency-ordered complex Hadamard transforms (SCHT) in a sliding window are presented. The first algorithm consists of decomposing a length-inverse SCHT (ISCHT) into two length-N/2 ISCHTs. The second algorithm, calculating the values of window i + N/4 from those of window i and one length-N/4 ISCHT and one length- N/4 Modified ISCHT (MISCHT), is implemented by two schemes to achieve a good compromise between the computation complexity and the implementation complexity. The forward SCHT algorithm can be obtained by transposing the signal flow graph of the ISCHT. The proposed algorithms require O(N) arithmetic operations and thus are more efficient than the block-based algorithms as well as those based on the sliding FFT or the sliding DFT. The application of the sliding ISCHT in transform domain adaptive filtering (TDAF) is also discussed with supporting simulation results.

关键词： Fast algorithm sequency-ordered complex Hadamard transform sliding algorithm

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Fast Hopping Discrete Sine Transform

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IEEE ACCESS 2021年 9卷 94293-94298页

作者： Kober, Vitaly Ctr Sci Res & Higher Educ Ensenada Ensenada 22860 Baja California Mexico Chelyabinsk State Univ Dept Math Chelyabinsk 454001 Russia Russian Acad Sci Inst Informat Transmiss Problems Moscow 127051 Russia

Discrete sine transform (DST) is widely used in digital signal processing such as image coding, spectral analysis, feature extraction, and filtering. This is because the discrete sine transform is close to the optimal Karhunen-Loeve transform for first-order Markov stationary signals with low correlation coefficients. Short-time (hopping) discrete sine transform can be employed for time-frequency analysis and adaptive processing quasi-stationary data such as speech, biomedical, radar and communication signals. Hopping transform refers to a transform computed on the signal of a fixed-size window that slides over the signal with an integer hop step. In this paper, we first derive a second-order recursive equation between DST spectra in equidistant signal windows, and then propose two fast algorithms for computing the hopping DST based on the recursive relationship and input-pruned DST algorithm. The performance of the proposed algorithms with respect to computational costs and execution time is compared with that of conventional sliding and fast DST algorithms. The computational complexity of the developed algorithms is lower than any of the existing algorithms, resulting in significant time savings.

关键词： Transforms Signal processing algorithms Discrete cosine transforms Time-frequency analysis Spectral analysis Laplace equations Correlation coefficient Discrete sine transform hopping algorithm short-time transform sliding algorithm signal processing

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Tower tableaux

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JOURNAL OF COMBINATORIAL THEORY SERIES A 2013年第4期120卷 843-871页

作者： Coskun, Olcay Taskin, Muge Bogazici Univ Matemat Bolumu TR-34342 Istanbul Turkey

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only for reduced words which makes the algorithm a test for reducibility. Using the algorithm, a bijection between tower diagrams and finite permutations is obtained and it is shown that this bijection specializes to a bijection between certain labellings of a given tower diagram and reduced expressions of the corresponding permutation. (c) 2013 Elsevier Inc. All rights reserved.

关键词： Reduced word Finite permutation Tower diagram sliding algorithm

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Fast Recursive Computation of sliding DHT with Arbitrary Step

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SENSORS 2020年第19期20卷 5556.-5556.页

作者： Kober, Vitaly CICESE Dept Comp Sci Ensenada 22860 Baja California Mexico Chelyabinsk State Univ Dept Math Chelyabinsk 454001 Russia Russian Acad Sci Inst Informat Transmiss Problems Moscow 127051 Russia

Short-time (sliding) transform based on discrete Hartley transform (DHT) is often used to estimate the power spectrum of a quasi-stationary process such as speech, audio, radar, communication, and biomedical signals. sliding transform calculates the transform coefficients of the signal in a fixed-size moving window. In order to speed up the spectral analysis of signals with slowly changing spectra, the window can slide along the signal with a step of more than one. A fast algorithm for computing the discrete Hartley transform in windows that are equidistant from each other is proposed. The algorithm is based on a second-order recursive relation between subsequent equidistant local transform spectra. The performance of the proposed algorithm with respect to computational complexity is compared with the performance of known fast Hartley transform and sliding algorithms.

关键词： discrete Hartley transform sliding algorithm sensor noise removal signal processing short-time transform

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Mit :: Ai :: Aim :: Aim-605

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2016年

Mit :: Ai :: Aim :: Aim-605 by published by

关键词： aim-605 algorithm algorithms artificial intelligence configuration configuration space convex convex hull cspace die obstacles safe paths slice projection slice projections sliding algorithm space obstacles spatial planning swept swept volume theorem vertices

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