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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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Controlling the light wavefront through a scattering medium based on direct digital frequency synthesis technology 被引量:1
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作者 Yuan Yuan Min-Yuan Sun +3 位作者 Yong Bi Wei-Nan Gao Shuo Zhang Wen-Ping Zhang 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第1期283-287,共5页
Phase modulation is a crucial step when the frequency-based wavefront optimization technique is exploited to measure the optical transmission matrix(TM) of a scattering medium. We report a simple but powerful method, ... Phase modulation is a crucial step when the frequency-based wavefront optimization technique is exploited to measure the optical transmission matrix(TM) of a scattering medium. We report a simple but powerful method, direct digital frequency synthesis(DDS) technology to modulate the phase front of the laser and measure the TM. By judiciously modulating the phase front of a He–Ne laser beam, we experimentally generate a high quality focus at any targeted location through a 2 mm thick 120 grit ground glass diffuser, which is commercially used in laser display and laser holographic display for improving brightness uniformity and reducing speckle. The signal to noise ratio(SNR) of the clear round focus is 50 and the size is about 44 μm. Our study will open up new avenues for enhancing light energy delivery to the optical engine in laser TV to lower the power consumption, phase compensation to reduce the speckle noise, and controlling the lasing threshold in random lasers. 展开更多
关键词 optical transmission matrix direct digital frequency synthesis technology phase modulation wavefront optimization
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EXACT ANALYSIS OF SPURIOUS SIGNALS IN DIRECT DIGITAL FREQUENCY SYNTHESIZERS DUE TO AMPLITUDE QUANTIZATION
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作者 Tian Xinguang Zhang Eryang 《Journal of Electronics(China)》 2009年第4期448-455,共8页
Amplitude quantization is one of the main sources of spurious noise frequencies in Direct Digital Frequency Synthesizers (DDFSs), which affect their application to many wireless telecommu- nication systems. In this pa... Amplitude quantization is one of the main sources of spurious noise frequencies in Direct Digital Frequency Synthesizers (DDFSs), which affect their application to many wireless telecommu- nication systems. In this paper, two different kinds of spurious signals due to amplitude quantization in DDFSs are exactly formulated in the time domain and detailedly compared in the frequency do- main, and the effects of the DDFS parameter variations on the spurious performance are thoroughly studied. Then the spectral properties and power levels of the amplitude-quantization spurs in the absence of phase-accumulator truncation are emphatically analyzed by waveform estimation and computer simulation, and several important conclusions are derived which can provide theoretical support for parameter choice and spurious performance evaluation in the application of DDFSs. 展开更多
关键词 Direct digital frequency Synthesizer (DDFS) SPUR Amplitude quantization Phase truncation
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Direct Digital Frequency Control Based on the Phase Step Change Characteristic between Signals
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作者 Zhao-Min Jia Xu-Hai Yang +3 位作者 Bao-Qi Sun Xiao-Ping Zhou Bo Xiang Xin-Yu Dou 《Chinese Physics Letters》 SCIE CAS CSCD 2017年第9期29-32,共4页
We present a new digital phase lock technology to achieve the frequency control and transformation through high precision multi-cycle group synchronization between signals without the frequency transformation circuit.... We present a new digital phase lock technology to achieve the frequency control and transformation through high precision multi-cycle group synchronization between signals without the frequency transformation circuit. In the case of digital sampling, the passing zero point of the phase of the controlled signal has the phase step characteristic, the phase step of the passing zero point is monotonic continuous with high resolution in the phase lock process, and using the border effect of digital fuzzy area, the gate can synchronize with the two signals, the quantization error is reduced. This technique is quite different from the existing methods of frequency transformation and frequency synthesis, the phase change characteristic between the periodic signals with different nominal is used. The phase change has the periodic phenomenon, and it has the high resolution step value. With the application of the physical law, the noise is reduced because of simplifying frequency transformation circuits, and the phase is locked with high precision. The regular phase change between frequency signals is only used for frequency measurement, and the change has evident randomness, but this randomness is greatly reduced in frequency control, and the certainty of the process result is clear. The experiment shows that the short term frequency stability can reach 10-12/s orders of magnitude. 展开更多
关键词 Direct digital frequency Control Based on the Phase Step Change Characteristic between Signals
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A high speed direct digital frequency synthesizer realized by a segmented nonlinear DAC
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作者 袁凌 倪卫宁 +2 位作者 郝志坤 石寅 李文昌 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2009年第9期66-69,共4页
This paper presents a high speed ROM-less direct digital frequency synthesizer (DDFS) which has a phase resolution of 32 bits and a magnitude resolution of 10 bits. A 10-bit nonlinear segmented DAC is used in place ... This paper presents a high speed ROM-less direct digital frequency synthesizer (DDFS) which has a phase resolution of 32 bits and a magnitude resolution of 10 bits. A 10-bit nonlinear segmented DAC is used in place of the ROM look-up table for phase-to-sine amplitude conversion and the linear DAC in a conventional DDFS. The design procedure for implementing the nonlinear DAC is presented. To ensure high speed, current mode logic (CML) is used. The chip is implemented in Chartered 0.35μm COMS technology with active area of 2.0 × 2.5 mm^2 and total power consumption of 400 mW at a single 3.3 V supply voltage. The maximum operating frequency is 850 MHz at room temperature and 1.0 GHz at 0℃. 展开更多
关键词 direct digital frequency synthesizer nonlinear DAC SEGMENTED ROM-less CML
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A 4 GHz 32 bit direct digital frequency synthesizer based on a novel architecture
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作者 武锦 陈建武 +4 位作者 吴旦昱 周磊 江帆 金智 刘新宇 《Journal of Semiconductors》 EI CAS CSCD 2013年第11期136-141,共6页
This paper presents a novel direct digital frequency synthesizer (DDFS) architecture based on nonlinear DAC coarse quantization and the ROM-based piecewise approximation method, which has the advantages of high spee... This paper presents a novel direct digital frequency synthesizer (DDFS) architecture based on nonlinear DAC coarse quantization and the ROM-based piecewise approximation method, which has the advantages of high speed, low power and low hardware resources. By subdividing the sinusoid into a collection of phase segments, the same initial value of each segment is realized by a nonlinear DAC. The ROM is decomposed with a coarse ROM and fine ROM using the piecewise approximation method. Then, the coarse ROM stores the offsets between the initial value of the common segment and the initial value of each line in the same segment. Meanwhile, the fine ROM stores the differences between the line values and the initial value of each line. A ROM compression ratio of 32 can be achieved in the case of 11 bit phase and 9 bit amplitude. Based on the above method, a prototype chip was fabricated using 1.4 #m GaAs HBT technology. The measurement shows an average spurious-free dynamic range (SFDR) of 45 dBc, with the worst SFDR only 40.07 dBc at a 4.0 GHz clock. The chip area is 4.6 × 3.7 mm2 and it consumes 7 W from a --4.9 V power supply. 展开更多
关键词 direct digital frequency synthesis read-only memory digital-to-analog converter gallium arsenide heterojunction bipolar transistor
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Novel analysis method for the spurious spectrum of direct digitalfrequency synthesizer in the presence of phase truncation
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作者 XieRenhong ShiXiangquan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第2期301-304,共4页
Based on the analysis of the spurious introduced by phase accumulation truncation which was made by Nicholas, a new simplified algorithm for spurious spectrum in the presence of phase truncation is presented by using ... Based on the analysis of the spurious introduced by phase accumulation truncation which was made by Nicholas, a new simplified algorithm for spurious spectrum in the presence of phase truncation is presented by using the mapping mathematics and number theoretic method, it is possible to precisely analyze the spurious location and the spurious amplitude introduced by phase truncation in practical applications by computer. 展开更多
关键词 direct digital frequency synthesis phase truncation SPURIOUS mapping.
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A high speed direct digital frequency synthesizer based on multi-channel structure
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作者 袁凌 张强 石寅 《Journal of Semiconductors》 EI CAS CSCD 2015年第6期131-135,共5页
This paper presents a direct digital frequency synthesizer (DDFS) for high speed application based on multi-channel structure. This DDFS has phase resolution of 32 bits and magnitude resolution of 12 bits. In order ... This paper presents a direct digital frequency synthesizer (DDFS) for high speed application based on multi-channel structure. This DDFS has phase resolution of 32 bits and magnitude resolution of 12 bits. In order to ensure the high speed and high resolution at the same time, the multi-channel sampling technique is used and a 12 bits linear digital-to-analog converter is implemented. The chip is fabricated in TSMC 130 nm CMOS technology with active area of 0.89 x 0.98 mm2 and total power consumption of 300 mW at a single 1.2 V supply voltage. The maximum operating speed is up to 2.0 GHz at room temperature. 展开更多
关键词 direct digital frequency synthesizer (DDFS) MULTI-CHANNEL phase-to-sine-amplitude converters(PSAC)
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A high-performance MUX-direct digital frequency synthesizer with quarter ROMs
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作者 Hao Zhikun Zhang Qiang +1 位作者 Ni weining Shi Yin 《Journal of Semiconductors》 EI CAS CSCD 2012年第1期127-130,共4页
This paper presents a detailed description of a high-performance direct digital frequency synthesizer (DDFS) using optimized quarter ROMs. To improve the working frequency and spectral purity, an original quarter RO... This paper presents a detailed description of a high-performance direct digital frequency synthesizer (DDFS) using optimized quarter ROMs. To improve the working frequency and spectral purity, an original quarter ROMs structure in 0.13 μm CMOS is brought forward and implemented. The working frequency is increased by 40% compared with Yuan Ling's methodIll of implementing a segmented DAC based DDFS. It has been implemented in 0.13 μm CMOS technology. The DDFS has a resolution of 10 bits with a measured SFDR 54 dBc. Its maximum operating frequency is 1.2 GHz by using six pipelining stages. Analytical investigation of improving spectral performances by using dual-slope approximation and pipeline is also presented. 展开更多
关键词 MUX-direct digital frequency synthesizers quarter ROMs dual-slope approximation
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Research for the Dynamic Range and Its Extension of Digital Intermediate Frequency Receiver
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作者 曹鹏 齐伟 费元春 《Journal of Beijing Institute of Technology》 EI CAS 2004年第4期381-384,共4页
For the optimization of dynamic range and bandwidth of digital intermediate frequency receiver(DIFR), main factors affecting them and their relationships are studied. Firstly, the DIFR sensitivity, bandwidth, noise fa... For the optimization of dynamic range and bandwidth of digital intermediate frequency receiver(DIFR), main factors affecting them and their relationships are studied. Firstly, the DIFR sensitivity, bandwidth, noise factor of radio frequency (RF) analog front-end (RFAF), and processing gain of intermediate frequency(IF) sampling are analyzed. Secondly, the constraint relationship of the noise factor of RFAF, the signal-to-noise ratio of ADC and the dynamic range of DIFR are studied. The relationship between the dynamic range and the RFAF gain, and that of the extended dynamic range and the RF AGC(automatic gain control) step are educed and simulated. These results can be used as theory foundations and design references for the implementation and optimization of the large dynamic range and wideband DIFR. 展开更多
关键词 BROADBAND sensitivity dynamic range digital intermediate frequency receivers(DIFR)
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A VERIFICATION ON DIVISION OF HYDROCLIMATIC AREA IN CHINA SEAS USING DIGITAL CHARACTERISTIC OF FREQUENCY DISTRIBUTION
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作者 Chen Shangji Li Binglan Yao Shiyu Du Bing National Marine Data and Information Service, SOA, Tianjin 300171 People’s Republic of China 《Journal of Geographical Sciences》 SCIE CSCD 1997年第3期83-90,共8页
oceanographic data files on the China Seas prepared by the National Marine Data and Information Service, SOA, China and the '30-year (1953-1982) Reports of Sea Surface Monthly Mean Temperature in the East China Se... oceanographic data files on the China Seas prepared by the National Marine Data and Information Service, SOA, China and the '30-year (1953-1982) Reports of Sea Surface Monthly Mean Temperature in the East China Sea by the Meteorological Agency, Japan,' were used to calculate the digital characteristics of frequency distribution of sea and air temperature in 153 areas in the China Seas. Principal factor analysis and fuzzy cluster ISODATA were used to divide the China hydroclimatic area into three climatic zones including ten climatic regions. It is concluded that the characteristic values derived by this method may completely show the characteristics of frequency distribution of sea and air temperature in the studied area and the final division of hydroclimatic area is fully coincident with the author's former result [2]. 展开更多
关键词 China Seas division of marine hydroclimatic area digital characteristic of frequency distribution principal factor analysis fuzzy cluster ISODATA.
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DDFS spurious signals due to amplitude quantization in absence of phase-accumulator truncation
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作者 Tian Xinguang Liu Xin +1 位作者 Chen Hong Duan Miyi 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第3期485-492,共8页
Spurious signals in direct digital frequency synthesizers (DDFSs) are partly caused by amplitude quantization and phase truncation, which affect their application to many wireless telecommunication systems. These si... Spurious signals in direct digital frequency synthesizers (DDFSs) are partly caused by amplitude quantization and phase truncation, which affect their application to many wireless telecommunication systems. These signals are deterministic and periodic in the time domain, so they appear as line spectra in the frequency domain. Two types of spurious signals due to amplitude quantization are exactly formulated and compared in the time and frequency domains respectively. Then the frequency spectra and power levels of the spurious signals due to amplitude quantization in the absence of phase-accumulator truncation are emphatically analyzed, and the effects of the DDFS parameter variations on the spurious signals are thoroughly studied by computer simulation. And several important conclusions are derived which can provide theoretical support for parameter choice and spurious performance evaluation in the application of DDFSs. 展开更多
关键词 spurious signal direct digital frequency synthesizer amplitude quantization phase truncation power level.
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New Developments in Maritime Communications: a Comprehensive Survey 被引量:7
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作者 Chen Weigang Yang Jinsheng +1 位作者 Ma Jianguo Li Si 《China Communications》 SCIE CSCD 2012年第2期31-42,共12页
This paper summarizes the requirements for modem maritime wireless communication networks in the marine environments including the sea- to-sea and sea-to-shore communication scenarios. The existing maritime wireless c... This paper summarizes the requirements for modem maritime wireless communication networks in the marine environments including the sea- to-sea and sea-to-shore communication scenarios. The existing maritime wireless communication sys- tems are presented and the development of the state-of-the-art maritime communication systems is surveyed. Furthermore, a hierarchical and integrated maritime network architecture is proposed to satisfy the increasing various classes of services which demand different Quality of Service (QoS). Finally, the open issues for further development of maritime communications are identified. 展开更多
关键词 maritime wireless communications dig-ital high frequency communications digital veryhigh frequency communications satellite communi-cations hierarchical and integrated maritime net-work
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ECCM schemes in netted radar system based ontemporal pulse diversity 被引量:1
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作者 ahmed abdalla zhao yuan bin tang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第5期1001-1009,共9页
For a netted radar system to counteract the deceptionelectronic countermeasure (ECM) signals, an effective electroniccounter countermeasure (ECCM) approach is proposed. The proposedapproach is realized based on th... For a netted radar system to counteract the deceptionelectronic countermeasure (ECM) signals, an effective electroniccounter countermeasure (ECCM) approach is proposed. The proposedapproach is realized based on the new signaling strategyfor the temporal pulse diversity, which makes use of transmittingpulses at each pulse repetition interval (PRI) with specific transmissionpulse block, and then following proper processing andinformation fusion. The existence of the deceptive ECM signal isconfirmed by one station, while the other stations in the nettedradar with same parameters applied the pulse diversity skillfully.Meanwhile, this method ensured that, pulse diversity can be appliedin netted radar. The performance assessment shows that theproposed solutions are effective in presence of ECM signals. Thisalgorithm has been demonstrated by simulations. The presentedsimulation results are in excellent consensus with theoretical predictions. 展开更多
关键词 pulse diversity electronic counter countermeasure(ECCM) digital radio frequency memory (DRFM) electronic countermeasure(ECM) netted radar matching filter.
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Development of capacitive sensor signal conditioning system for angular displacement measurement using timer IC LM555 and UFDC 被引量:2
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作者 Sumitesh Majumder T K Maiti 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2019年第1期49-54,共6页
In this research paper,we have presented variable area type capacitive sensor signal conditioning system for angular displacement measurement and for this purpose we have used timer LM555 based astable multivibrator a... In this research paper,we have presented variable area type capacitive sensor signal conditioning system for angular displacement measurement and for this purpose we have used timer LM555 based astable multivibrator and universal frequency to digital converter (UFDC). Due to variation in angular displacement in the variable area type capacitor which is connected in the timer based astable circuit,capacitance changes which in turn changes the time period of the timer circuit output. The time period of the timer output waveform is linear with the capacitance and hence linear with angular displacement. The timer output is further processed with UFDC for the measurement. The experimental results show that the time period is linear with the angular displacement in the range of 0- 180° and the uncertainty we should associate it with this average time period value is the standard deviation of the mean,often called the standard error (SE),which is ± 0.023 μs. Because of the simplicity,this measurement system can be used in both electronic and industrial instrumentation. 展开更多
关键词 variable area type capacitive sensor timer circuit sensor interfacing astable multivibrator universal frequency to digital converter (UFDC)
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Origin, Alternative Expressions of Newcomb-Benford Law and Deviations of Digit Frequencies
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作者 Gene Whyman 《Applied Mathematics》 2021年第7期576-586,共11页
The Newcomb-Benford law, which describes the uneven distribution of the frequencies of digits in data sets, is by its nature probabilistic. Therefore, the main goal of this work was to derive formulas for the permissi... The Newcomb-Benford law, which describes the uneven distribution of the frequencies of digits in data sets, is by its nature probabilistic. Therefore, the main goal of this work was to derive formulas for the permissible deviations of the above frequencies (confidence intervals). For this, a previously developed method was used, which represents an alternative to the traditional approach. The alternative formula expressing the Newcomb-Benford law is re-derived. As shown in general form, it is numerically equivalent to the original Benford formula. The obtained formulas for confidence intervals for Benford’s law are shown to be useful for checking arrays of numerical data. Consequences for numeral systems with different bases are analyzed. The alternative expression for the frequencies of digits at the second decimal place is deduced together with the corresponding deviation intervals. In general, in this approach, all the presented results are a consequence of the positionality property of digital systems such as decimal, binary, etc. 展开更多
关键词 Benford’s Law Confidence Intervals in Benford’s Law Alternative Expression of Benford’s Law Benford’s Law for Different Numeral Systems Frequencies of Digits at the Second Decimal Place
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Digital output compensation for precise frequency transfer over commercial fiber link
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作者 慈骋 吴虹 +5 位作者 唐然 刘波 陈星 章学松 张瑜 赵迎新 《Optoelectronics Letters》 EI 2018年第2期109-113,共5页
An ultra-highly precise and long-term stable frequency transmission system over 120 km commercial fiber link has been proposed and experimentally demonstrated. This system is based on digital output compensation techn... An ultra-highly precise and long-term stable frequency transmission system over 120 km commercial fiber link has been proposed and experimentally demonstrated. This system is based on digital output compensation technique to suppress phase fluctuations during the frequency transmission process. A mode-locked erbium-doped fiber laser driven by a hydrogen maser serves as an optical transmitter. Moreover, a dense wavelength division multiplexing system is able to separate forward and backward signals with reflection effect excluded. The ultimate fractional frequency instabilities for the long-distance frequency distributed system are up to 3.14×10^(-15) at 1 s and 2.96×10^(-19) at 10 000 s, respectively. 展开更多
关键词 digital output compensation for precise frequency transfer over commercial fiber link
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Compact and effective photon-resolved image scanning microscope
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作者 Giorgio Tortarolo Alessandro Zunino +5 位作者 Simonluca Piazza Mattia Donato Sabrina Zappone Agnieszka Pierzyńska-Mach Marco Castello Giuseppe Vicidomini 《Advanced Photonics》 SCIE EI CAS CSCD 2024年第1期84-95,共12页
Fluorescence confocal laser-scanning microscopy(LSM)is one of the most popular tools for life science research.This popularity is expected to grow thanks to single-photon array detectors tailored for LSM.These detecto... Fluorescence confocal laser-scanning microscopy(LSM)is one of the most popular tools for life science research.This popularity is expected to grow thanks to single-photon array detectors tailored for LSM.These detectors offer unique single-photon spatiotemporal information,opening new perspectives for gentle and quantitative superresolution imaging.However,a flawless recording of this information poses significant challenges for the microscope data acquisition(DAQ)system.We present a DAQ module based on the digital frequency domain principle,able to record essential spatial and temporal features of photons.We use this module to extend the capabilities of established imaging techniques based on single-photon avalanche diode(SPAD)array detectors,such as fluorescence lifetime image scanning microscopy.Furthermore,we use the module to introduce a robust multispecies approach encoding the fluorophore excitation spectra in the time domain.Finally,we combine time-resolved stimulated emission depletion microscopy with image scanning microscopy,boosting spatial resolution.Our results demonstrate how a conventional fluorescence laser scanning microscope can transform into a simple,information-rich,superresolved imaging system with the simple addition of a SPAD array detector with a tailored data acquisition system.We expected a blooming of advanced single-photon imaging techniques,which effectively harness all the sample information encoded in each photon. 展开更多
关键词 fluorescence lifetime image scanning microscopy digital frequency domain single photon
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A reconfigurable OTA-C baseband filter with wide digital tuning for GNSS receivers
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作者 潘文光 马成炎 +1 位作者 甘业兵 叶甜春 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2010年第9期94-98,共5页
The design of a digitally-tunable sixth-order reconfigurable OTA-C filter in a 0.18-μm RFCMOS process is proposed.The filter can be configured as a complex band pass filter or two real low pass filters.An improved di... The design of a digitally-tunable sixth-order reconfigurable OTA-C filter in a 0.18-μm RFCMOS process is proposed.The filter can be configured as a complex band pass filter or two real low pass filters.An improved digital automatic frequency tuning scheme based on the voltage controlled oscillator technique is adopted to compensate for process variations.An extended tuning range(above 8:1) is obtained by using widely continuously tunable transconductors based on digital techniques.In the complex band pass mode,the bandwidth can be tuned from 3 to 24 MHz and the center frequency from 3 to 16 MHz. 展开更多
关键词 reconfigurable filter wide tuning digital frequency tuning
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Fractional Fourier domain analysis of decimation and interpolation 被引量:15
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作者 MENG XiangYi TAO Ran WANG Yue 《Science in China(Series F)》 2007年第4期521-538,共18页
The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signal... The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal. Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security. Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital frequency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sampling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations. 展开更多
关键词 DECIMATION INTERPOLATION fractional Fourier transform sampling rate conversion the digital frequency in the fractional Fourier domain
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