WO2015131396A1 - Procédé d'échantillonnage aléatoire de signal unidimensionnel sur la base d'une détection compressée - Google Patents

Procédé d'échantillonnage aléatoire de signal unidimensionnel sur la base d'une détection compressée Download PDF

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Publication number
WO2015131396A1
WO2015131396A1 PCT/CN2014/073054 CN2014073054W WO2015131396A1 WO 2015131396 A1 WO2015131396 A1 WO 2015131396A1 CN 2014073054 W CN2014073054 W CN 2014073054W WO 2015131396 A1 WO2015131396 A1 WO 2015131396A1
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WIPO (PCT)
Prior art keywords
signal
value
sawtooth wave
compressed sensing
wave voltage
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PCT/CN2014/073054
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English (en)
Chinese (zh)
Inventor
李冬梅
罗庆
梁圣法
李小静
张�浩
谢常青
刘明
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中国科学院微电子研究所
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Priority to PCT/CN2014/073054 priority Critical patent/WO2015131396A1/fr
Publication of WO2015131396A1 publication Critical patent/WO2015131396A1/fr

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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/3059—Digital compression and data reduction techniques where the original information is represented by a subset or similar information, e.g. lossy compression
    • H03M7/3062—Compressive sampling or sensing

Definitions

  • the present invention relates to the field of signal acquisition technologies, and in particular, to a method for randomly sampling a one-dimensional signal based on compressed sensing.
  • Step 1 Using the measurement matrix ⁇ to observe the original signal X, project the n-dimensional signal to the m-dimensional, where m ⁇ n .
  • the observation matrix ⁇ gives the original signal X.
  • the measurement matrix ⁇ in the above method is a Gaussian random matrix, and the construction process of the Gaussian random matrix requires that the value of each position in the Gaussian random matrix is a random number that conforms to the Gaussian distribution, which is currently not realized in hardware, which leads to The above method is difficult to implement in hardware, and this method is only suitable for mathematical simulation, which is far from practical application.
  • the main object of the present invention is to provide a one-dimensional signal random sampling method based on compressed sensing.
  • the present invention provides a one-dimensional signal random sampling method based on compressed sensing, the method comprising:
  • Step 1 The sawtooth voltage signal generator generates n sawtooth voltage signals numbered 1, 2, 3...n, where n is a natural number;
  • Step 2 The comparator compares the n sawtooth voltage signals with the input signal, determines the time point k and the voltage value y at the intersection of the sawtooth wave voltage signal and the input signal, and constructs the observation matrix ⁇ by using the time point k.
  • the n-sawtooth voltage signals in step 1 have the same peak-to-peak value and period, and the peak-to-peak value is ⁇ , and the initial voltages of the respective sawtooth wave voltage signals are 0, A, 2 ⁇ , 3 ⁇ , respectively. .. ( ⁇ -1 ) ⁇ .
  • the comparator in step 2 compares the n sawtooth voltage signals with the input signal to determine a time point k and a voltage value y at the intersection of the sawtooth voltage signal and the input signal, including: The n sawtooth voltage signals are simultaneously compared with an input signal having an amplitude of (n-1) A, and the time point k and the voltage value y at the intersection of the sawtooth voltage signal and the input signal are recorded.
  • the time point k is obtained by counting, and a counter connected to the comparator starts counting when the first sawtooth wave voltage signal is generated by the sawtooth wave voltage signal generator, and records the sawtooth wave voltage signal and Enter the count value at the intersection of the signals.
  • the measured value Y in the form of a matrix is composed of y m
  • Specific steps include:
  • the method for random sampling of one-dimensional signal based on compressed sensing adopts a method of comparing an input signal with a sawtooth voltage signal, and artificially controls the frequency of the sawtooth wave signal under the premise of satisfying the requirement of the compressed sensing measurement matrix.
  • the number of y m actually sampled is lower than the number of sampling points at the Nyquist frequency, and the reconstruction of the signal X is applied by the compression sensing theory, so it can be used for hardware-implemented sampling below the Nyquist frequency. .
  • the present invention provides a one-dimensional signal random sampling method based on compressed sensing, because the system output value k m k passes the formula
  • the one-dimensional signal random sampling method based on compressed sensing provided by the invention utilizes the feature that the input signal is unknown at the next moment, and skillfully designs a random sampling method, which only utilizes the sampling frequency while reducing the sampling frequency.
  • the sawtooth voltage signal generator, comparator, and counter implement a simplified sampling circuit that reduces the pressure on the data acquisition side for acquisition, storage, and transmission.
  • the one-dimensional signal random sampling method based on compressed sensing provided by the present invention reduces the error of each sampling point y m by a method of comparing the multi-channel sawtooth wave with one input signal by a method of one sawtooth wave. l/n, solves the problem of the sawtooth wave error, so it can be applied to the sampling field with higher precision requirements.
  • the one-dimensional signal random sampling method based on compressed sensing provided by the present invention is more suitable for large-area use because of simple implementation, simplified sampling circuit, less stored data, and low power consumption.
  • FIG. 1 is a schematic diagram of a basic frame for constructing compressed sensing based on a one-dimensional signal random sampling method based on compressed sensing according to an embodiment of the present invention
  • FIG. 2 is a flowchart of a one-dimensional signal random sampling method based on compressed sensing according to an embodiment of the present invention
  • FIG. 3 is a schematic diagram of a one-dimensional signal random sampling method based on compressed sensing according to an embodiment of the present invention
  • FIG. 4 is a schematic diagram of error analysis of a one-dimensional signal random sampling method based on compressed sensing according to an embodiment of the present invention
  • FIG. 5 is a schematic diagram of an initial concept of a one-dimensional signal random sampling method based on compressed sensing according to an embodiment of the present invention
  • FIG. 6 is a schematic diagram showing changes of a relative error of increasing points of a one-dimensional signal random sampling method based on compressed sensing according to an embodiment of the present invention
  • FIG. 7 is a schematic diagram of an improved hardware implementation of a one-dimensional signal random sampling method based on compressed sensing according to an embodiment of the present invention
  • FIG. 8 is a schematic diagram of an improved hardware implementation of a one-dimensional signal random sampling method based on compressed sensing according to an embodiment of the invention.
  • the randomly sampled measurement matrix is a matrix obtained by randomly extracting m rows from an n-dimensional unit matrix from the extracted m rows.
  • the matrix satisfies the requirements that are not related to the sparse basis.
  • FIG. 2 is a flowchart of a method for randomly sampling a one-dimensional signal based on compressed sensing according to an embodiment of the present invention, the method comprising:
  • Step 1 The sawtooth voltage signal generator generates n sawtooth voltage signals numbered 1, 2, 3...n, respectively, n is a natural number; wherein, the n sawtooth voltage signals have peak-to-peak values The same as the period, the peak-to-peak value is A, and the initial voltages of the respective sawtooth voltage signals are 0, A, 2A, 3A... (n-1) A, respectively.
  • Step 2 The comparator compares the n sawtooth voltage signals with the input signal, determines the time point k and the voltage value y at the intersection of the sawtooth wave voltage signal and the input signal, and constructs the observation matrix ⁇ by using the time point k.
  • the comparator compares the n sawtooth wave voltage signals with the input signal to determine a time point k and a voltage value y at an intersection of the sawtooth wave voltage signal and the input signal, including: the comparator simultaneously simultaneously nth the sawtooth wave voltage signals In contrast to an input signal having an amplitude within (n-1) A, the time point k and the voltage value y at the intersection of the sawtooth voltage signal and the input signal are recorded.
  • the time point k is obtained by counting, and a counter connected to the comparator starts counting when the sawtooth wave voltage signal generator generates the first sawtooth wave voltage signal, and records the intersection of the sawtooth wave voltage signal and the input signal.
  • the maximum value is also the number of sampling points in the case of full sampling of the original signal, and j is a sign of the complex number.
  • y m constitutes a measured value Y in the form of a matrix.
  • the first concept of the present invention is to generate a sawtooth voltage signal as shown in FIG. 5, and generate the sawtooth voltage signal with an input having an amplitude within (n-1) A.
  • the signals are compared, the abscissa is the count point, and the count values ⁇ , 13 ⁇ 4, k 3 , 13 ⁇ 4, k 5 k m at the intersection are recorded.
  • the counting frequency of the counter is / , where ⁇ is the time when the Nyquist frequency is sampled. Interval.
  • the present invention improves the implementation method of the hardware circuit, as shown in FIG. 7 and FIG. 8, before the improvement, FIG. 7 compares the input signal with the single sawtooth wave, and the improved FIG. 8 shows the input signal and the multi-channel sawtooth wave.
  • FIG. 7 compares the input signal with the single sawtooth wave
  • FIG. 8 shows the input signal and the multi-channel sawtooth wave.
  • an additional judgment unit is obtained, and the result of FIG. 3 is obtained.
  • a judging unit is added to judge whether the intersection point is generated by the input signal and which sawtooth voltage signal, and the formula is the determination of c in the formula (4).
  • the sawtooth voltage signal generator is used to generate n sawtooth voltage signals numbered 1, 2, 3...n, respectively, and the peak-to-peak and period of the sawtooth voltage signal are the same, peak-to-peak For A, the initial voltage of each sawtooth voltage signal is 0, A, 2A, 3A... (n-1) A, respectively.
  • a comparator for simultaneously generating the generated n-channel sawtooth voltage signal with an amplitude of (n-1)
  • the counter starts to count evenly from the start of the system operation, and outputs the current count value to the signal transmission unit when the sawtooth voltage signal is equal to the input signal.
  • the determining unit is configured to determine which of the ⁇ -channel sawtooth voltage signals is equal to the input signal to determine the y m value of the point.
  • the signal transmission unit is used for signal adjustment and input, that is, the output signal of the sensor is adjusted to a suitable amplitude range (less than nA) and then to the next comparison.
  • the input signal P is compared with the quad sawtooth voltage signal at the same time. Record the count value of the intersection point, where the value offord still uses the formula (3) to, and the expression becomes
  • y m cA + (k m mod a)b where c 6 ⁇ 0,1,2,3... ⁇
  • the main advantage of the circuit shown in Figure 8 is that the error is reduced.
  • the error of the L-channel sawtooth is 1/L of the error before the improvement, which solves the problem of the inherent error of the original system and makes it closer to the actual application. At the same time, it does not bring too much burden to the hardware circuit, so the hardware requirements of this design are very low, which is very suitable for the application of sensor network nodes.
  • OMP Orthogonal Matching Pursuit
  • Orthogonal Matching Pursuit is the earliest One of the greedy iterative algorithms.
  • the algorithm follows the atomic selection criterion in the matching pursuit algorithm, only orthogonalizes the set of selected atoms by recursion to ensure the optimality of the iteration, thus reducing the number of iterations.
  • the OMP algorithm effectively overcomes the problem that the matching pursuit algorithm often needs to go through a large number of iterations in order to obtain a good convergence effect.
  • the OMP algorithm orthogonalizes the selected atoms using the Gram-Schmidt orthogonalization method, and then projects the signals on the space formed by these orthogonal atoms to obtain the components and margins of the signals on the selected atoms, and then uses the same
  • the method decomposes the margin.
  • the selected atoms satisfy certain conditions, so the margin decreases rapidly with the decomposition process.
  • the iterative optimality is ensured by recursively orthogonalizing the set of selected atoms, thereby reducing the number of iterations.
  • the OMP reconstruction algorithm is reconstructed for a given number of iterations. This forced iterative process stops so that OMP requires a lot of linear measurements to ensure accurate reconstruction. In short, it selects the column of ⁇ in a greedy iterative way, so that the selected column in each iteration is most correlated with the current redundant vector, subtracting the relevant part from the measurement vector and iterating iteratively until the number of iterations reaches The sparsity K, forcing the iteration to stop.
  • gases such as ammonia, carbon dioxide, etc.
  • the senor uses a sensor of ammonia concentration
  • the output signal is a voltage value
  • the sampling circuit is a circuit designed by the sampling method of the invention
  • the output voltage signal of the ammonia concentration sensor is an input signal of the sampling circuit.
  • the first parameter the input signal is compared with the generated sawtooth voltage signal from the sampling point, and a trigger signal is generated when the sawtooth voltage signal intersects with the input signal, and the electric
  • the counter portion of the road is also counting.
  • Second ⁇ The trigger signal reaches the counter section to record the current count.
  • the third parameter According to the recorded count, the input signal value at the intersection is calculated by the formula (4), and the observation matrix is obtained by the received count and the formula (3), and the obtained count is k m , formula (3) Only k m is an unknown quantity, and ⁇ can be obtained by substituting.
  • Part IV Reconstruct the original signal by the ⁇ algorithm to complete the signal acquisition.

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  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Measuring Fluid Pressure (AREA)

Abstract

L'invention concerne un procédé d'échantillonnage aléatoire de signal unidimensionnel sur la base d'une détection compressée. Le procédé consiste : en ce qu'un générateur de signal de tension en dents de scie génère un nombre n de signaux de tension en dents de scie, les numéros de série des signaux de tension en dents de scie allant de un à n, et n étant un nombre naturel ; en ce que le nombre n de signaux de tension en dents de scie et des signaux d'entrée sont comparés au moyen d'un comparateur, en ce que les points temporels k et les valeurs de tension y aux points d'intersection des signaux de tension en dents de scie et des signaux d'entrée sont déterminés, en ce qu'une matrice de mesure Φ est construite au moyen des points temporels k, en ce que la valeur de mesure Y d'un signal original est construite au moyen des valeurs de tension y, et donc qu'une équation d'échantillonnage de compression Y = ΦX est construite, X étant le signal original et Y étant la valeur de mesure du signal original ; en ce que l'équation d'échantillonnage de compression Y = ΦX est reconstruite au moyen d'un algorithme de récupération dans la théorie de détection compressée, et en ce que le signal original X est obtenu en fonction de la valeur de mesure Y et de la matrice de mesure Φ. Grâce à l'invention, les signaux peuvent être reconstruits dans un mode à haute probabilité à un faible taux d'échantillonnage moyen, la limite de fréquence de Nyquist est dépassée, le besoin en matériel est réduit, et le coût et la difficulté de mise en œuvre matérielle sont réduits.
PCT/CN2014/073054 2014-03-07 2014-03-07 Procédé d'échantillonnage aléatoire de signal unidimensionnel sur la base d'une détection compressée WO2015131396A1 (fr)

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Cited By (4)

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CN107332566A (zh) * 2017-06-19 2017-11-07 四川大学 基于mwc的支撑集快速恢复方法
WO2018032368A1 (fr) * 2016-08-13 2018-02-22 深圳市樊溪电子有限公司 Procédé de traitement de données de système de chaîne de blocs sur la base d'une acquisition comprimée et d'un algorithme de reconstruction creuse
CN109088638A (zh) * 2018-08-15 2018-12-25 苏州蛟视智能科技有限公司 一种基于二进制测量矩阵的压缩感知方法
FR3079976A1 (fr) * 2018-04-09 2019-10-11 Safran Module d'acquisition pour un systeme de surveillance d'une machine tournante, systeme et procede de surveillance

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CN102253117A (zh) * 2011-03-31 2011-11-23 浙江大学 一种基于压缩感知的新型声学信号采集方法
CN103346798A (zh) * 2013-06-05 2013-10-09 中国科学院微电子研究所 一种以低于奈奎斯特频率的采样频率进行信号采集方法
CN103595414A (zh) * 2012-08-15 2014-02-19 王景芳 一种稀疏采样与信号压缩感知重构方法

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US7345603B1 (en) * 2006-11-07 2008-03-18 L3 Communications Integrated Systems, L.P. Method and apparatus for compressed sensing using analog projection
WO2011060816A1 (fr) * 2009-11-18 2011-05-26 Nokia Corporation Traitement de données
CN102253117A (zh) * 2011-03-31 2011-11-23 浙江大学 一种基于压缩感知的新型声学信号采集方法
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Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018032368A1 (fr) * 2016-08-13 2018-02-22 深圳市樊溪电子有限公司 Procédé de traitement de données de système de chaîne de blocs sur la base d'une acquisition comprimée et d'un algorithme de reconstruction creuse
CN107332566A (zh) * 2017-06-19 2017-11-07 四川大学 基于mwc的支撑集快速恢复方法
CN107332566B (zh) * 2017-06-19 2020-09-08 四川大学 基于mwc的支撑集快速恢复方法
FR3079976A1 (fr) * 2018-04-09 2019-10-11 Safran Module d'acquisition pour un systeme de surveillance d'une machine tournante, systeme et procede de surveillance
WO2019197220A1 (fr) 2018-04-09 2019-10-17 Safran Module d'acquisition pour un systeme de surveillance d'une machine tournante, systeme et procede de surveillance
CN112154314A (zh) * 2018-04-09 2020-12-29 赛峰集团 用于旋转机构的信号采集模块、监测系统、飞机和监测旋转机构的方法
US11280701B2 (en) 2018-04-09 2022-03-22 Safran Acquisition module for a system for monitoring a rotating machine, monitoring system and method
CN112154314B (zh) * 2018-04-09 2022-10-11 赛峰集团 用于旋转机构的信号采集模块、监测系统、飞机和监测旋转机构的方法
CN109088638A (zh) * 2018-08-15 2018-12-25 苏州蛟视智能科技有限公司 一种基于二进制测量矩阵的压缩感知方法

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