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Automatic modulation recognition of radiation source signals based on two-dimensional data matrix and improved residual neural network
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作者 Guanghua Yi Xinhong Hao +3 位作者 Xiaopeng Yan Jian Dai Yangtian Liu Yanwen Han 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第3期364-373,共10页
Automatic modulation recognition(AMR)of radiation source signals is a research focus in the field of cognitive radio.However,the AMR of radiation source signals at low SNRs still faces a great challenge.Therefore,the ... Automatic modulation recognition(AMR)of radiation source signals is a research focus in the field of cognitive radio.However,the AMR of radiation source signals at low SNRs still faces a great challenge.Therefore,the AMR method of radiation source signals based on two-dimensional data matrix and improved residual neural network is proposed in this paper.First,the time series of the radiation source signals are reconstructed into two-dimensional data matrix,which greatly simplifies the signal preprocessing process.Second,the depthwise convolution and large-size convolutional kernels based residual neural network(DLRNet)is proposed to improve the feature extraction capability of the AMR model.Finally,the model performs feature extraction and classification on the two-dimensional data matrix to obtain the recognition vector that represents the signal modulation type.Theoretical analysis and simulation results show that the AMR method based on two-dimensional data matrix and improved residual network can significantly improve the accuracy of the AMR method.The recognition accuracy of the proposed method maintains a high level greater than 90% even at -14 dB SNR. 展开更多
关键词 Automatic modulation recognition Radiation source signals Two-dimensional data matrix Residual neural network Depthwise convolution
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Research on Modulation Signal Denoising Method Based on Improved Variational Mode Decomposition
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作者 Canyu Mo Qianqiang Lin +1 位作者 Yuanduo Niu Haoran Du 《Journal of Electronic Research and Application》 2024年第1期7-15,共9页
In order to further analyze the micro-motion modulation signals generated by rotating components and extract micro-motion features,a modulation signal denoising algorithm based on improved variational mode decompositi... In order to further analyze the micro-motion modulation signals generated by rotating components and extract micro-motion features,a modulation signal denoising algorithm based on improved variational mode decomposition(VMD)is proposed.To improve the time-frequency performance,this method decomposes the data into narrowband signals and analyzes the internal energy and frequency variations within the signal.Genetic algorithms are used to adaptively optimize the mode number and bandwidth control parameters in the process of VMD.This approach aims to obtain the optimal parameter combination and perform mode decomposition on the micro-motion modulation signal.The optimal mode number and quadratic penalty factor for VMD are determined.Based on the optimal values of the mode number and quadratic penalty factor,the original signal is decomposed using VMD,resulting in optimal mode number intrinsic mode function(IMF)components.The effective modes are then reconstructed with the denoised modes,achieving signal denoising.Through experimental data verification,the proposed algorithm demonstrates effective denoising of modulation signals.In simulation data validation,the algorithm achieves the highest signal-to-noise ratio(SNR)and exhibits the best performance. 展开更多
关键词 Micro-motion modulation signal Variational mode decomposition Genetic algorithm Adaptive optimization
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A new tracking error detection method using amplitude difference detection for signal waveform modulation multi-level discs 被引量:1
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作者 严明铭 裴京 潘龙法 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第10期319-323,共5页
The sub-land/sub-pit affects the characteristic of the tracking error signal which is generated by the conventional differential phase detection (DPD) method in the signal waveform modulation multi-level (SWML) re... The sub-land/sub-pit affects the characteristic of the tracking error signal which is generated by the conventional differential phase detection (DPD) method in the signal waveform modulation multi-level (SWML) read-only disc. To solve this problem, this paper proposes a new tracking error detection method using amplitude difference. Based on the diffraction theory, the amplitude difference is proportional to the tracking error and is feasible to be used for obtaining the off-track information. The experimental system of the amplitude difference detection method is developed. The experimental results show that the tracking error signal derived from the new method has better performance in uniformity and signal-to-noise ratio than that derived from the conventional DPD method in the SWML read-only disc. 展开更多
关键词 signal waveform modulation multi-level technology tracking error amplitude difference
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Improved partial response maximum likelihood method combining modulation code for signal waveform modulation multi-level disc
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作者 王鹤群 裴京 潘龙法 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第10期213-219,共7页
In this paper, we describe an improved adaptive partial response maximum likelihood (PRML) method combining modulation code tbr signal waveform modulation multi-level disc. This improved adaptive PRML method employs... In this paper, we describe an improved adaptive partial response maximum likelihood (PRML) method combining modulation code tbr signal waveform modulation multi-level disc. This improved adaptive PRML method employs partial response equalizer and adaptive viterbi detector combining modulation code. Compared with the traditional adaptive PRML detector, the improved PRML detector additionally employs illogical sequence detector and corrector. Illogical sequence detector and corrector can aw)id the appearance of illogical sequences effectively, which do not follow the law of modulation code for signal waveform modulation multi-level disc, and obtain the correct sequences. We implement the improved PRML detector using a DSP and an FPGA chip. The experimental results show good performance. The higher efficient and lower complexity can be obtained by using the improved PRML method than by using the previous PRML method. Meanwhile, resource utilization of the improved PRML detector is not changed, but the bit error rate (BER) is reduced by more than 20%. 展开更多
关键词 multi-level disc signal waveform modulation viterbi detector partial response maximum likeli-hood
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Read channel for signal waveform modulation multi-level disc
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作者 王鹤群 徐海峥 +1 位作者 潘龙法 刘海龙 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第12期334-338,共5页
A novel read channel for signal waveform modulation multi-level disc is presented in this paper. This read channel employs timing recovery system and partial response maximum likelihood detector. Compared to the previ... A novel read channel for signal waveform modulation multi-level disc is presented in this paper. This read channel employs timing recovery system and partial response maximum likelihood detector. Compared to the previous read channel composed of level detection and run-length detection, the present read channel shows superiority in capacity increase and robust performance. Especially, relying on the partial response maximum likelihood detection, lower bit error rate can be obtained. 展开更多
关键词 multi-level disc signal waveform modulation read channel partial response maximum likelihood
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Modulation recognition of communication signals based on SCHKS-SSVM 被引量:5
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作者 Xiaolin Zhang Jian Chen Zhiguo Sun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第4期627-633,共7页
A novel modulation recognition algorithm is proposed by introducing a Chen-Harker-Kanzow-Smale (CHKS) smooth function into the C-support vector machine deformation algorithm. A set of seven characteristic parameters i... A novel modulation recognition algorithm is proposed by introducing a Chen-Harker-Kanzow-Smale (CHKS) smooth function into the C-support vector machine deformation algorithm. A set of seven characteristic parameters is selected from a range of parameters of communication signals including instantaneous amplitude, phase, and frequency. And the Newton-Armijo algorithm is utilized to train the proposed algorithm, namely, smooth CHKS smooth support vector machine (SCHKS-SSVM). Compared with the existing algorithms, the proposed algorithm not only solves the non-differentiable problem of the second order objective function, but also reduces the recognition error. It significantly improves the training speed and also saves a large amount of storage space through large-scale sorting problems. The simulation results show that the recognition rate of the algorithm can batch training. Therefore, the proposed algorithm is suitable for solving the problem of high dimension and its recognition can exceed 95% when the signal-to-noise ratio is no less than 10 dB. 展开更多
关键词 communication signal modulation recognition support vector machine smooth function
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Stochastic Resonance in a Single-Mode Laser Driven by Quadratic Colored Pump Noise:Effects of Biased Amplitude Modulation Signal 被引量:8
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作者 ZHANG Liang-Ying CAO Li WU Da-Jin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第7期143-148,共6页
A single-mode laser noise model driven by quadratic colored pump noise and biased amplitude modulationsignal is proposed.The analytic expression of signal-to-noise ratio is calculated by using a new linearized procedu... A single-mode laser noise model driven by quadratic colored pump noise and biased amplitude modulationsignal is proposed.The analytic expression of signal-to-noise ratio is calculated by using a new linearized procedure.Itis found that there are three different typies of stochastic resonance in the model:the conventional form of stochasticresonance,the stochastic resonance in the broad sense,and the bona fide SR. 展开更多
关键词 stochastic resonance quadratic colored pump noise bias amplitude modulation signal
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Design of Irregular QC-LDPC Code Based Multi-Level Coded Modulation Scheme for High Speed Optical Communication Systems 被引量:7
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作者 Liqian Wang Dongdong Wang +3 位作者 Yongjing Ni Xue Chen Midou Cui Fu Yang 《China Communications》 SCIE CSCD 2019年第5期106-120,共15页
In this paper, we focus on the design of irregular QC-LDPC code based multi-level coded modulation(MLCM) scheme by jointly optimizing the component code rate and the degree distribution of the irregular QC-LDPC compon... In this paper, we focus on the design of irregular QC-LDPC code based multi-level coded modulation(MLCM) scheme by jointly optimizing the component code rate and the degree distribution of the irregular QC-LDPC component code. Firstly, the sub-channel capacities of MLCM systems is analyzed and discussed, based on which the optimal component code rate can be obtained. Secondly, an extrinsic information transfer chart based two-stage searching algorithm is proposed to find the good irregular QC-LDPC code ensembles with optimal component code rates for their corresponding sub-channels. Finally, by constructing the irregular QC-LDPC component codes from the designed ensembles with the aim of possibly enlarging the girth and reducing the number of the shortest cycles, the designed irregular QC-LDPC code based 16QAM and 64QAM MLCM systems can achieve 0.4 dB and 1.2 dB net coding gain, respectively, compared with the recently proposed regular QC-LDPC code based 16QAM and 64QAM MLCM systems. 展开更多
关键词 quasi-cyclic LOW-DENSITY parity check (QC-LDPC) code irregular extrinsic INFORMATION transfer(EXIT) chart generalized mutual information(GMI) multi-level coded modulation(MLCM)
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Modulation recognition of MIMO radar signal based on joint HOS and SNR algorithm 被引量:3
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作者 Xiaojing Wang Ying Xiong +1 位作者 Yunhao Li Bin Tang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第2期226-236,共11页
This paper presents a joint high order statistics (HOS) and signal-to-noise ratio (SNR) algorithm for the recognition of multiple-input multiple-output (MIMO) radar signal without a priori knowledge of the signa... This paper presents a joint high order statistics (HOS) and signal-to-noise ratio (SNR) algorithm for the recognition of multiple-input multiple-output (MIMO) radar signal without a priori knowledge of the signal parameters. This method is capable of recognizing the MIMO radar signal as well as discriminating it from single-carrier signal adopted by conventional radar. Meanwhile, the sub-carrier number of the none-coding MIMO radar signal is estimated. Extensive simulations are carried out in different operating conditions. Simulation results prove the feasibility and indicate that the recognition probability could reach over 90% when the value of SNR is above 0 dB. 展开更多
关键词 modulation recognition multiple-input multiple-output(MIMO) radar signal high order statistics (HOS).
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A new method of demodulating the digital frequency modulation signals 被引量:2
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作者 Jin-cai Sun Wei-jie Zhu Yi-yun Sun and Hui Xiao 《Journal of Marine Science and Application》 2003年第2期5-10,共6页
A new method of estimating the frequency-known signals from the strong background noise was presented first. Then the new method was used in the demodulation of the digital frequency modulation (FSK) signals. The new ... A new method of estimating the frequency-known signals from the strong background noise was presented first. Then the new method was used in the demodulation of the digital frequency modulation (FSK) signals. The new demodulation method can complete the demodulation of the FSK signals only with the carrier frequency and without any carrier phase information. The simulation results show that the performance of anti-noise of the new method is better than that of the incoherent demodulation method and the fluctuation of the carrier phase has little effect on the new method. So the new demodulation method has a fine prospect in the practical applications. 展开更多
关键词 digital frequency modulation signals underwater acoustic communications DEmodulation DETECTION
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Stochastic Resonance in Linear Region of a Single-Mode Laser: Effects of Amplitude Modulation of Signal 被引量:1
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作者 ZHANG Liang-Ying CAO Li WU Da-Jin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第5期1310-1314,共5页
A single-mode laser noise model driven by quadratic colored pump noise and amplitude modulation signal is proposed. The real and imaginary parts of the pump noise are assumed to be cross-correlation. The effect of cro... A single-mode laser noise model driven by quadratic colored pump noise and amplitude modulation signal is proposed. The real and imaginary parts of the pump noise are assumed to be cross-correlation. The effect of cross- correlation of noise and amplitude modulation of signal on laser statistical properties is studied by using the linearized approximation. The analytic expression of signal-to-noise ratio (SNR) is calculated. It is found that the phenomena of stochastic resonance (SR) respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λ and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency ω in our model. It is shown that there are three different typies of SR in the model: the conventional form of SR, the SR in the broad sense, and the bona fide SR. 展开更多
关键词 stochastic resonance single-mode laser amplitude modulation signal
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Effect on Intensity Correlation Time by Input Signal in a Single-Mode Laser with Bias Signal Modulation 被引量:1
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作者 CHEN Li-Mei CAO Li +1 位作者 WU Da-Jin GE Guo-Qin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4X期638-642,共5页
The effect on intensity correlation time T by input signal is studied for gain-noise model of a single-mode laser driven by colored pump noise and colored quantum noise with colored cross-correlation with a bias signa... The effect on intensity correlation time T by input signal is studied for gain-noise model of a single-mode laser driven by colored pump noise and colored quantum noise with colored cross-correlation with a bias signal modulation in this paper. By using the linear approximation method, we detect that there exists maximum (i.e., resonance) in the curve of the intensity correlation time T upon bias current io when the noise correlation coefficient λ is positive; and there exists minimum (i.e., suppression) in the T-io curve when λ is negative. And whenλ is zero, T increases monotonously with increasing io. Furthermore, the curve of T upon the signal frequency Ω is also studied. Our study shows that no matter what the value of λ is, there exists minimum (i.e., suppression) in the T-Ω curve. 展开更多
关键词 intensity correlation time bias signal modulation linear approximation method
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Dual-Use Signal Design for Radar and Communication via Joint Orthogonal Signal and Phase Modulation 被引量:1
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作者 Yu Lin Yi Bu +3 位作者 Hui Qiu Xue Yao Xianxiang Yu Guolong Cui 《Journal of Beijing Institute of Technology》 EI CAS 2021年第1期20-30,共11页
This paper proposes a new information modulation resorting to orthogonal signal and its phase for dual-function radar communication(DFRC)systems.Focusing on the standardized linear frequency modulation(LFM)signal by a... This paper proposes a new information modulation resorting to orthogonal signal and its phase for dual-function radar communication(DFRC)systems.Focusing on the standardized linear frequency modulation(LFM)signal by additional phase,a bank of signals enjoying satisfactory autocorrelation and cross-correlation characteristics,are generated.Then,these signals map the different information as well as their phases are also modulated to increase the communication bit rate,thus yielding a series of dual-use signals.Finally,the radar detection and communication performance of dual-use signals are also provided through numerical simulation and half-physical platform verification,confirming the effectiveness of the designed signals compared with the existing design strategy. 展开更多
关键词 dual-function radar communication(DFRC) dual-use signal joint orthoganal signal and phase modulation
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A novel M-ary modulation technique based on optimal chirp signal design 被引量:1
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作者 孟繁宇 Gu Xuemai Guo Qing 《High Technology Letters》 EI CAS 2012年第4期357-363,共7页
A novel M-ary chirp modulation technique based on an optimal chirp signal design is proposed in this paper to offer higher data rate for an indoor wireless chirp spread spectrum communication system. Both linear chirp... A novel M-ary chirp modulation technique based on an optimal chirp signal design is proposed in this paper to offer higher data rate for an indoor wireless chirp spread spectrum communication system. Both linear chirp signals and combined chirp signals are used in this system to reduce the effect of the cross correlation, and simplify the complexity of the system. The optimal scheme of de- signing both linear chirp signals and combined chirp signals is discussed to minimize the value of the cross correlation and obtain a better system performance. Simulation results show that, compared with the binary orthogonal chirp modulation technique, the M-ary chirp modulation technique based on an optimal chirp signal set has a higher data rate with a reasonable bit-error rate (BER) perform- ance under both additive white gaussian noise (AWGN) channel and indoor wireless channel. 展开更多
关键词 M-ary modulation chirp spread spectrum combined chirp signal indoor wirelesschannel
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IMMUNE RBF NETWORK AND ITS APPLICATION IN THE MODULATION-STYLE RECOGNITION OF RADAR SIGNALS 被引量:1
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作者 Gong Xinbao Zang Xiaogang Zhou Xilang Hu Guangrui (Dept. of Electronic Eng., Shanghai Jiaotong Univ., Shanghai 200030) 《Journal of Electronics(China)》 2003年第5期378-382,共5页
Based on Immune Programming(IP), a novel Radial Basis Function (RBF) networkdesigning method is proposed. Through extracting the preliminary knowledge about the widthof the basis function as the vaccine to form the im... Based on Immune Programming(IP), a novel Radial Basis Function (RBF) networkdesigning method is proposed. Through extracting the preliminary knowledge about the widthof the basis function as the vaccine to form the immune operator, the algorithm reduces thesearching space of canonical algorithm and improves the convergence speed. The application ofthe RBF network trained with the algorithm in the modulation-style recognition of radar signalsdemonstrates that the network has a fast convergence speed with good performances. 展开更多
关键词 Immune programming Immune operator Radial basis function network Analog modulated radar signals
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Blind parameter estimation of pseudo-random binary code-linear frequency modulation signal based on Duffing oscillator at low SNR 被引量:1
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作者 Ke Wang Xiaopeng Yan† +2 位作者 Ze Li Xinhong Hao Honghai Yu 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第5期312-319,共8页
Conventional parameter estimation methods for pseudo-random binary code-linear frequency modulation(PRBC-LFM)signals require prior knowledge,are computationally complex,and exhibit poor performance at low signal-to-no... Conventional parameter estimation methods for pseudo-random binary code-linear frequency modulation(PRBC-LFM)signals require prior knowledge,are computationally complex,and exhibit poor performance at low signal-to-noise ratios(SNRs).To overcome these problems,a blind parameter estimation method based on a Duffing oscillator array is proposed.A new relationship formula among the state of the Duffing oscillator,the pseudo-random sequence of the PRBC-LFM signal,and the frequency difference between the PRBC-LFM signal and the periodic driving force signal of the Duffing oscillator is derived,providing the theoretical basis for blind parameter estimation.Methods based on amplitude method,short-time Fourier transform method,and power spectrum entropy method are used to binarize the output of the Duffing oscillator array,and their performance is compared.The pseudo-random sequence is estimated using Duffing oscillator array synchronization,and the carrier frequency parameters are obtained by the relational expressions and characteristics of the difference frequency.Simulation results show that this blind estimation method overcomes limitations in prior knowledge and maintains good parameter estimation performance up to an SNR of-35 dB. 展开更多
关键词 Duffing oscillator pseudo-random binary code-linear frequency modulation(PRBC-LFM)signal blind parameter estimation low signal-to-noise ratio(SNR)
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DESIGN OF INTERPOLATION FILTER FOR ALL DIGITAL RECEIVER-ON THE INTERPOLATION PROBLEM OF FULL RESPONSE MODULATION SIGNALS
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作者 Fan Pingyi Feng Chongxi(Department of Electronic Engineering, Tsinghua University, Beijng 100084) 《Journal of Electronics(China)》 1998年第2期150-157,共8页
All digital implementation of receiver is a main topic on digital communication recently. The design of interpolation filter is one of the important problems for all digital implementation of receiver. In this paper, ... All digital implementation of receiver is a main topic on digital communication recently. The design of interpolation filter is one of the important problems for all digital implementation of receiver. In this paper, for full response linear modulation signal, a interpolation criterion is proposed. An interpolation formula is presented on bandwidth-limited transmission signal. For example, using the raised cosine roll off function as the system pulse response, the feasibility and effectiveness on the interpolation formula are certified by theoretical and numerical analysis. The computer simulation result on 16-QAM signal is given. 展开更多
关键词 ALL digital RECEIVER INTERPOLATION filter Full RESPONSE modulation signal
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Research of Hybrid Modulation Radar Signal
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作者 Kai-Feng Guo Yun Lin +1 位作者 Meng Wang Xiao-Chun Xu 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2013年第3期35-39,共5页
Based on the advantage of phase coded signal and stepped frequency signal,a new hybrid modulation signal is introduced in this paper. It combines phase code modulation during the pulse with stepped frequency modulatio... Based on the advantage of phase coded signal and stepped frequency signal,a new hybrid modulation signal is introduced in this paper. It combines phase code modulation during the pulse with stepped frequency modulation between the pulses, which is named as phase-coded stepped-frequency ( PCSF ) signal. By analyzing its waveform and ambiguity function,the comparison between Stepped-Frequency ( SF) signal and PCSF signal is given,which shows that the PCSF signal is better than SF signal. Finally,the signal processing method with two stage compressed processing is presented. The simulation results show that this new hybrid modulation radar signal can get a higher stepped frequency than ordinary SF signal,realize the same equivalent bandwidth with less pulse number,and solve the conflict among the stepped frequency,the number of pulse, and transmit average power. Under the premises of a certain range resolution,this new hybrid modulation radar signal not only raises the data rate of radar system,but also reduces Doppler sensitivity with a good prospect, and the effect of one-dimensional range profile is much better than that of traditional SF signal. Therefore,this new hybrid modulation radar signal can be widely used in application. 展开更多
关键词 phase coded stepped frequency hybrid modulation signal ambiguity function signal processing
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Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator
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作者 刘立 张良英 曹力 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第10期4182-4186,共5页
The diffusion in a harmonic oscillator driven by coloured noises ξ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expre... The diffusion in a harmonic oscillator driven by coloured noises ξ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time z3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient A of the two Ornstein-Uhlenbeck (O-U) noises. 2) Changing the value of T3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model. 展开更多
关键词 coloured cross-correlation cross-correlation coefficient diffusion coefficient signal modulated noise noise-induced transition
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Transfer characteristics of dynamic biochemical signals in non-reversing pulsatile flows in a shallow Y-shaped microfluidic channel: signal filtering and nonlinear amplitude-frequency modulation
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作者 Zongzheng CHEN Weimo YUAN +4 位作者 A.R.AZIZ Zhengming GAO Depei ZENG Bo LIU Kairong QIN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2017年第10期1481-1496,共16页
The transports of the dynamic biochemical signals in the non-reversing pulsatile flows in the mixing microchannel of a Y-shaped microfluidic device are ana- lyzed. The results show that the mixing micro-channel acts a... The transports of the dynamic biochemical signals in the non-reversing pulsatile flows in the mixing microchannel of a Y-shaped microfluidic device are ana- lyzed. The results show that the mixing micro-channel acts as a low-pass filter, and the biochemical signals are nonlinearly modulated by the pulsatile flows, which depend on the biochemical signal frequency, the flow signal frequency, and the biochemical signal transporting distance. It is concluded that, the transfer characteristics of the dynamic biochemical signals, which are transported in the time-varying flows, should be carefully considered for better loading biochemical signals on the cells cultured on the bottom of the microfluidic channel. 展开更多
关键词 shallow Y-shaped microfluidic channel dynamic biochemical signal non-reversing pulsatile flow nonlinear amplitude-frequency modulation Taylor-Aris disper-sion
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