WO2015006898A1 - 适用于一维缓变信号的随机采样器 - Google Patents

适用于一维缓变信号的随机采样器 Download PDF

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Publication number
WO2015006898A1
WO2015006898A1 PCT/CN2013/079363 CN2013079363W WO2015006898A1 WO 2015006898 A1 WO2015006898 A1 WO 2015006898A1 CN 2013079363 W CN2013079363 W CN 2013079363W WO 2015006898 A1 WO2015006898 A1 WO 2015006898A1
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signal
unit
sawtooth wave
slope
output
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PCT/CN2013/079363
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English (en)
French (fr)
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李冬梅
罗庆
梁圣法
杨洪璋
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 US14/888,335 priority Critical patent/US9762217B2/en
Priority to PCT/CN2013/079363 priority patent/WO2015006898A1/zh
Publication of WO2015006898A1 publication Critical patent/WO2015006898A1/zh

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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03K—PULSE TECHNIQUE
    • H03K4/00—Generating pulses having essentially a finite slope or stepped portions
    • H03K4/06—Generating pulses having essentially a finite slope or stepped portions having triangular shape
    • H03K4/08—Generating pulses having essentially a finite slope or stepped portions having triangular shape having sawtooth shape
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03K—PULSE TECHNIQUE
    • H03K3/00—Circuits for generating electric pulses; Monostable, bistable or multistable circuits
    • H03K3/84—Generating pulses having a predetermined statistical distribution of a parameter, e.g. random pulse generators
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03K—PULSE TECHNIQUE
    • H03K4/00—Generating pulses having essentially a finite slope or stepped portions
    • H03K4/06—Generating pulses having essentially a finite slope or stepped portions having triangular shape
    • H03K4/08—Generating pulses having essentially a finite slope or stepped portions having triangular shape having sawtooth shape
    • H03K4/48—Generating pulses having essentially a finite slope or stepped portions having triangular shape having sawtooth shape using as active elements semiconductor devices
    • H03K4/50—Generating pulses having essentially a finite slope or stepped portions having triangular shape having sawtooth shape using as active elements semiconductor devices in which a sawtooth voltage is produced across a capacitor

Definitions

  • the present invention relates to the field of signal acquisition technologies, and in particular, to a random sampler suitable for a one-dimensional slowly varying signal.
  • a sampler below the Nyquist frequency is called an Analog to Information Converter (AIC).
  • the analog information converter uses a pseudo-random sequence mixing random sampler, as shown in Figure 1. As shown, the random sampler first mixes the input sparse signal with a pseudo-random sequence, and then uses a conventional periodic sampled sampler to low-frequency sample the signal, and the output signal is sent to a subsequent compressed sensing algorithm.
  • the analog information converter simply aliases the input signal through a sequence consisting of +1-1, and does not really achieve random sampling, and the hardware complexity is relatively high, requiring a certain storage space; Slowly varying signals, mixing increases the complexity of the signal, so random sampling of one-dimensional slowly varying signals is not applicable.
  • the present invention provides a random sampler suitable for one-dimensional slowly varying signals, to solve the problem of high complexity of the random sampling circuit, and to achieve simplicity.
  • the purpose of the circuit is to overcome the defects of the prior art described above.
  • the present invention provides a random sampler suitable for a one-dimensional slowly varying signal, the random sampler comprising a signal pre-processing unit 1, a slope-controllable sawtooth wave signal generating unit 2, a signal comparing unit 3, Counting unit 4 and signal transmitting unit 5, wherein:
  • the signal pre-processing unit 1 is configured to pre-process the input signal, and transmit the pre-processed input signal to the signal comparison unit 3;
  • the slope-controllable sawtooth wave signal generating unit 2 is configured to generate a sawtooth wave signal with a controllable slope, and implement a clearing process, and the sawtooth wave signal is sent to the signal comparing unit 3;
  • the signal comparison unit 3 is configured to compare the input signal input by the signal pre-processing unit 1 with the sawtooth wave signal generated by the slope-controllable sawtooth wave generating unit 2, and output the pulse signal to the slope-controllable sawtooth wave when the two are the same Generation unit 2 and signal transmission unit 5;
  • the counting unit 4 is configured to start counting the clock signal while the sawtooth wave signal generating unit 2 generates the sawtooth wave signal, and transmit the signal to the signal output unit 5;
  • the signal output unit 5 is configured to output the number counted by the counting unit 4 at the time after receiving the pulse signal output from the signal comparison unit 3.
  • the signal pre-processing unit 1 pre-processes the input signal, and performs inverse processing on the input signal to acquire more data in case of abrupt changes, thereby improving the average sampling rate.
  • the sawtooth wave signal generated by the slope-controllable sawtooth wave signal generating unit 2 is sent to the signal comparing unit 3, and compared with the preprocessed input signal in the signal comparing unit 3, when the two are equal
  • the signal comparison unit 3 outputs a pulse signal to the slope-controllable sawtooth wave signal generation unit 2, and the slope-controllable sawtooth wave generation unit 2 is cleared to regenerate a new sawtooth wave signal.
  • the sawtooth wave generating unit 2 with adjustable slope includes a constant current source, a capacitor and a switch triggered by the pulse signal, and the slope of the sawtooth signal is controlled by adjusting the current of the constant current source.
  • a pulse-triggered switch is used to clear the sawtooth signal voltage.
  • the signal comparison unit 3 is composed of a comparator, and the slope is controllable.
  • the sawtooth wave signal generated by the sawtooth wave generating unit 2 and the input signal preprocessed by the signal preprocessing unit 1 are respectively input from the comparator positive input terminal and the negative input terminal, and when the sawtooth wave signal is smaller than the input signal, the comparator output is The terminal is low, when the sawtooth signal is equal to the input signal or greater than the input signal, the output of the comparator is high, and the output pulse signal is sent to the slope controllable sawtooth generating unit 2 and the signal transmission unit 5, the slope
  • the controllable sawtooth wave generating unit 2 is cleared to start a new sawtooth wave signal generation, and the signal transmission unit 5 outputs the current count.
  • the counting unit 4 is implemented by a counter, and the number of the counter includes time point information and voltage magnitude information of the sawtooth wave signal, and is used for data recovery by a computer connected to the output end of the signal output unit 5.
  • the excitation signal of the signal output unit 5 is a pulse signal generated by the signal comparison unit 3, and the output of the signal output unit 5 is an instantaneous number generated by the counting unit 4.
  • the present invention has the following beneficial effects:
  • the random sampler provided by the present invention does not require a storage unit, does not require an AD sampler, and does not require a conventional sampling mode compression processing unit, so there is no need to store data to save hardware cost and work. Consumption, low hardware complexity, real random sampling, more suitable for the acquisition of one-dimensional slowly varying signals.
  • the random sampler provided by the invention reduces the sampling frequency by applying the principle of compressed sensing, and realizes sampling lower than the Nyquist frequency under the premise of reconstructing the original signal.
  • An example is as follows: Suppose that a signal needs to take ten points in one second according to the Nyquist frequency sampling, and sampling with the random sampler provided by the present invention can control two to three points in one second, because the present invention
  • the sampling time point is determined by the sawtooth wave and the input signal.
  • the two signals are compared every time, one point is recorded, that is, the smaller the slope of the sawtooth wave is, the lower the sampling frequency is, so as to realize the sampling frequency.
  • Compressed sensing is a theoretical basis. In the case of low sampling rate, only the requirements of compressed sensing are met, and the signal can be reconstructed by compressing the sensing algorithm.
  • the random sampler provided by the invention has lower hardware complexity, is lower than the traditional mode and the AIC sampler, and is easier to implement, reducing hardware cost and reducing system power consumption. 4.
  • the random sampler provided by the invention not only does not need to perform mixing, but the mixing increases the complexity of the signal, so it is more suitable for the acquisition of one-dimensional slowly varying signals without increasing the complexity of the signal.
  • the random sampler provided by the present invention compared with the AIC system, the measurement matrix of the AIC system needs to know the values of all pseudo-random sequences, and then determines which part of the interception is to determine the measurement matrix, and the measurement matrix of the present invention. As long as the value of the counter is received, the sampling matrix is easier to determine, and the signal collected by it is easier to reconstruct using the compressed sensing method.
  • the random sampler provided by the present invention outputs a count generated by a counter, and does not need to be stored before being sent, thereby saving storage space.
  • FIG. 1 is a schematic structural view of a random sampler in the prior art
  • FIG. 2 is a block diagram showing a structure of a random sampler suitable for a one-dimensionally graded signal according to an embodiment of the present invention
  • Figure 3 is a schematic diagram of the effect to be achieved by the signal pre-processing unit of Figure 2;
  • FIG. 4 is a schematic structural diagram of a sawtooth wave signal generating unit with a slope controllable in FIG. 2;
  • FIG. 5 is a comparison of a random sampled data by a random sampler provided by the present invention, and a comparison between the restored signal and the original signal by the OMP algorithm based on the compressed sensing. .
  • the random sampler provided by the present invention is completely different from the AIC sampler shown in FIG. 1.
  • the AIC sampler shown in FIG. 1 mixes the signal and then samples the low speed.
  • the method realizes random sampling of signals; and the random sampler provided by the present invention uses randomness of intersections of two signals to realize random sampling of signals. Since the present invention does not mix signals, there is no Increasing the complexity of the signal, and the differences in implementation principles described above, result in completely different hardware implementations.
  • FIG. 2 is a schematic structural diagram of a random sampler suitable for a one-dimensional slow-changing signal, which includes a signal pre-processing unit 1, and a slope-controllable sawtooth wave signal generating unit according to an embodiment of the invention. 2.
  • Signal comparison unit 3 counting unit 4 and signal transmission unit 5.
  • the pulse signal output from the signal comparison unit 3 is used to control the sawtooth wave signal generation unit 2 and the signal transmission unit 5 whose slope is controllable. The details are described below for each part.
  • the signal pre-processing unit 1 is configured to pre-process the input signal before the input signal reaches the signal comparison unit 3, and transmit the pre-processed input signal to the signal comparison unit 3 to enable more acquisition in case of a sudden change.
  • Data increasing the average sampling rate; where the preprocessing is to invert the input signal.
  • the present invention preprocesses the signal and inverts it so that the signal with increasing intensity can be better sampled.
  • the random sampler provided by the invention increases the data acquisition frequency when the signal is close to zero, and the sudden change of the sensor signal is usually a positive direction change. The actual requirement is to collect more data when there is a change, so the collected data needs to be performed.
  • Pre-processing this pre-processing is mainly to invert the input signal. The expected effect is shown in Figure 3. It can be seen that the signal on the right is the inversion of the signal on the left.
  • the slope-controllable sawtooth wave signal generating unit 2 is configured to generate a slope-controllable sawtooth wave signal and implement a clearing process, the sawtooth wave signal is supplied to the signal comparison unit 3, and is preprocessed in the signal comparison unit 3
  • the input signals are compared, the pulses are output when the two are equal, and the sawtooth generation unit 2 whose slope is controllable is cleared, the new sawtooth signal is regenerated, and the above actions are repeated, the purpose of which is to provide random sampling provided by the present invention.
  • the sawtooth wave signal generated by the device itself is compared with the input signal, and a random pulse is generated by using the randomness of the equal case, and then the characteristic signals of the equal points are used by the counter and the signal transmission unit.
  • the information is transmitted to a computer connected to the output of the signal transmission unit 5, and then restored by a reconstruction algorithm of the compressed sensing theory.
  • the M sample values are the matrix of the acquired signals, and the left side is the product of the original signal J and the coefficient matrix, and the coefficient matrix is used to sparse and measure the original signal.
  • the signal output by the counter obtained by the invention includes the information of the measurement matrix and the measured value information, and the sparse matrix can be customized, so the basic underdetermined equation of the compressed sensing has been constructed, and the scientific community has a relatively mature solution.
  • the algorithm of the underdetermined equation can be directly applied. For details, refer to the common signal reconstruction algorithm below.
  • the slope of the sawtooth wave is lower, and the slope of the sawtooth wave signal determines the average sampling rate of the random sampling. Different signals are required to ensure that the slope of the sawtooth signal is adjustable.
  • the schematic diagram of the sawtooth wave generating unit with adjustable slope includes a constant current source, a capacitor and a switch triggered by the pulse signal.
  • the slope of the sawtooth signal is controlled by adjusting the current of the constant current source, and the sawtooth signal voltage is cleared by a pulse-triggered switch.
  • Compressed sensing is a new theory of information acquisition. It is a method of signal acquisition and reconstruction based on signal sparse representation, measurement matrix non-correlation and approximation theory. The theory states that as long as the signal is sparse or compressed at a certain base time, the structural information of the signal can be obtained by a sampling rate much lower than that required by the Nyquist sampling theorem, and the signal can be accurately refined by the reconstruction algorithm. Refactoring. Compressed sensing theory only needs to consist of two parts: projecting the signal on the observation vector to obtain the observed value, and reconstructing the signal from the observed value using the reconstruction algorithm.
  • ⁇ be a signal of length N, whose sparsity is ( ⁇ ⁇ ⁇ , sparsity means that ⁇ itself has ⁇ non-zero elements, or the expansion coefficient in a certain variation domain has ⁇ non-zero elements.
  • Signal ⁇ (assuming the signal is in the transform domain ⁇ ⁇ coefficient)
  • the key to reconstructing the signal is to find the sparse representation of the signal ⁇ in the ⁇ domain, which can be passed /.
  • the norm optimization problem finds a solution with a coefficient structure:
  • Common signal reconstruction algorithms include a minimum norm model, a matching pursuit algorithm, and an orthogonal matching pursuit algorithm, where:
  • the matching tracking sparse reconstruction algorithm solves the minimum norm problem.
  • the basic idea of the matching pursuit algorithm is to select the atom that best matches the signal from the overcomplete atomic library (ie, the perceptual matrix:) to perform the sparse approximation and find the margin in each iteration. Then continue to select the atom that best matches the signal margin. After several iterations, the signal can be represented linearly by some atoms. However, since the non-orthogonality of the projection of the signal on the set of selected atoms (the column vector of the perceptual matrix) makes the result of each iteration likely to be suboptimal, it is often necessary to obtain more convergence effects. The number of iterations.
  • the matching tracking algorithm calculates the correlation coefficient by finding the absolute value of the inner product between the residual r and the individual atoms in the perceptual matrix ⁇ u:
  • the signal approximation and margin update are performed using the least squares method:
  • Orthogonal Matching Pursuit is one of the earliest greedy iterative algorithms.
  • the algorithm follows the atomic selection criterion in the matching pursuit algorithm, and only orthogonalizes the set of selected atoms by recursion to ensure the optimality of the iteration, thus reducing the number of iterations.
  • the ⁇ 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 ⁇ algorithm uses the Gram-Schmidt orthogonalization method for orthogonal processing and then projects the signal on the space formed by these orthogonal atoms to obtain the components and residuals of the signal on each selected atom, and then use the same method. Decompose the margin. In each decomposition, 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 Sparseness, forced iteration to stop.
  • the signal comparison unit 3 is configured to compare the input signal input by the signal pre-processing unit 1 with the sawtooth wave signal generated by the slope-controllable sawtooth wave generating unit 2, and output the pulse signal to the slope-controllable sawtooth wave when the two are the same.
  • the unit 2 and the signal transmission unit 5 are used for the zeroing of the slope-controllable sawtooth wave generating unit 2 and the processing of the signal transmission unit 5.
  • the signal comparison unit 3 is the simplest and most core part of the hardware implementation of the random sampler provided by the present invention.
  • the present invention mainly utilizes the comparison of the sawtooth wave signal generated by the sawtooth wave generation unit 2 with the slope controllable with the input signal to realize randomization. The generation of the pulse signal, thus realizing random sampling in the true sense.
  • the signal comparison unit 3 is mainly composed of a comparator, and the sawtooth wave signal generated by the slope-controllable sawtooth wave generating unit 2 and the input signal preprocessed by the signal preprocessing unit 1 are input from the comparator positive input terminal and the negative input terminal, respectively.
  • the output of the comparator is low.
  • the output of the comparator is high.
  • the sawtooth signal generating unit A new sawtooth signal is generated starting from zero.
  • the signal transmission unit 5 outputs the current count to the computer.
  • the counting unit 4 is configured to start counting the clock signal while the sawtooth wave signal generating unit 2 generates the sawtooth wave signal, and transmit the signal to the signal output unit 5; the counting unit 4 is generally implemented by using a counter due to the slope of the sawtooth wave signal. It is known that the number of this counter contains time point information and voltage magnitude information of the sawtooth signal. The counter number contains two main pieces of information for data recovery on the computer side. The frequency of the clock signal here can be adjusted to ensure the recovery of the final signal.
  • signal output unit 5 is configured to output a digitally counted number of the counting unit 4 to the computer after receiving the pulse signal output from the signal comparison unit 3, the computer being connected to the signal output unit 5.
  • the excitation signal of the signal transmission unit 5 is a pulse signal generated by the signal comparison unit 3, and the output is the real-time number generated by the counting unit 4.
  • the simulation of the acquisition and recovery of the gas sensor signal by using the random sampling method can be found that the random sampling method is feasible within a certain error tolerance range.
  • Figure 5 a random sampled signal recovery comparison chart.
  • the random sampler provided by the present invention truly realizes random acquisition of signals in the time domain, and has real randomness, because the AIC sampler mixing shown in FIG. Pseudo-random sequences are used, not true random mixing.
  • the random sampler provided by the present invention has no memory portion, no pseudo-random sequence generator portion, no ADC chip, and the circuit is simpler and easier to implement, thereby saving storage space and power consumption.

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Abstract

本发明公开了一种适用于一维缓变信号的随机采样器，包括：信号预处理单元，用于对输入信号进行预处理；斜率可控的锯齿波信号发生单元，用于生成斜率可控的锯齿波信号，并实现清零处理；信号比较单元，用于将信号预处理单元输入的输入信号与斜率可控的锯齿波发生单元生成的锯齿波信号进行比较，在二者相同时输出脉冲信号给斜率可控的锯齿波发生单元和信号传输单元；计数单元，用于在锯齿波信号发生单元生成锯齿波信号的同时对时钟信号开始计数，并传输给信号输出单元；信号输出单元，用于在接收到信号比较单元输出的脉冲信号后输出计数单元当时计数的数字。本发明的随机采样器有采样率低，硬件复杂度低，易于实现并且不占用存储空间的特点。

Description

适用于一维缓变信号的随机采样器
技术领域 本发明涉及信号采集技术领域， 特别涉及一种适用于一维缓变信号 的随机采样器。
背景技术 传统的信号采样通常采用固定频率的周期采样， 遵循奈奎斯特
(Nyquist)采样定理， 采样率的最小值为信号带宽的两倍。 这种采样方 法虽然能够保证信号较为完美的恢复， 但是在一定程度上浪费了硬件资 源以及存储空间。 近些年随着压缩感知的提出， 打破了奈奎斯特定律的 限制， 开始探索低于奈奎斯特频率的采样方法。
目前存在的一种低于奈奎斯特频率的采样器被称作模拟信息转换 器 （Analog to Information Converter, AIC)， 该模拟信息转换器采用伪 随机序列混频的随机采样器， 如图 1所示， 该随机采样器先利用伪随机 序列对输入的稀疏信号进行混频， 然后再采用传统周期采样的积分采样 器对信号进行低频率采样， 输出信号送给后续的压缩感知算法。
但是该模拟信息转换器只是通过 +1-1 组成的序列对输入信号进行 混叠， 并没有真正实现随机的采样， 同时硬件复杂度相对较高， 需要一 定的存储空间； 再者， 针对一维缓变信号， 混频会增加信号的复杂度， 所以并不适用一维缓变信号的随机采样。
因此， 需要提出一种更加适用于一维缓变信号的随机采样器。
发明内容
(一） 要解决的技术问题
为了克服上述现有技术存在的缺陷， 本发明提供了一种适用于一维 缓变信号的随机采样器， 以解决随机采样电路复杂度高的问题， 达到简 化电路的目的。
(二） 技术方案
为达到上述目的， 本发明提供了一种适用于一维缓变信号的随机采 样器， 该随机采样器包括信号预处理单元 1、 斜率可控的锯齿波信号发 生单元 2、 信号比较单元 3、 计数单元 4和信号传输单元 5， 其中：
信号预处理单元 1， 用于对输入信号进行预处理， 并将预处理后的 输入信号传输给信号比较单元 3 ;
斜率可控的锯齿波信号发生单元 2， 用于生成斜率可控的锯齿波信 号， 并实现清零处理， 该锯齿波信号被输送给信号比较单元 3 ;
信号比较单元 3， 用于将信号预处理单元 1输入的输入信号与斜率 可控的锯齿波发生单元 2生成的锯齿波信号进行比较， 在二者相同时输 出脉冲信号给斜率可控的锯齿波发生单元 2和信号传输单元 5;
计数单元 4， 用于在锯齿波信号发生单元 2生成锯齿波信号的同时 对时钟信号开始计数， 并传输给信号输出单元 5;
信号输出单元 5， 用于在接收到信号比较单元 3输出的脉冲信号后 输出计数单元 4当时计数的数字。
上述方案中， 所述信号预处理单元 1对输入信号进行预处理， 是对 输入信号进行反转处理， 以在有突变的情况下能够更多地采集数据， 提 高平均采样率。
上述方案中， 所述斜率可控的锯齿波信号发生单元 2生成的锯齿波 信号被输送给信号比较单元 3， 在信号比较单元 3中与经过预处理的输 入信号进行比较， 在二者相等时信号比较单元 3输出脉冲信号给斜率可 控的锯齿波信号发生单元 2， 斜率可控的锯齿波发生单元 2清零， 重新 产生新的锯齿波信号。
上述方案中， 所述斜率可调的锯齿波发生单元 2包括一个恒流源、 一个电容和一个由脉冲信号触发的开关， 通过调节恒流源的电流大小来 控制锯齿波信号的斜率， 通过由脉冲触发的开关来对锯齿波信号电压进 行清零。
上述方案中， 所述信号比较单元 3由一个比较器构成， 斜率可控的 锯齿波发生单元 2生成的锯齿波信号与经过信号预处理单元 1预处理后 的输入信号分别从比较器正输入端和负输入端输入， 当锯齿波信号小于 输入信号时， 该比较器的输出端为低电平， 当锯齿波信号等于输入信号 或者大于输入信号时， 该比较器的输出端为高电平， 输出脉冲信号给斜 率可控的锯齿波发生单元 2和信号传输单元 5， 斜率可控的锯齿波发生 单元 2被清零开始新一次的锯齿波信号生成， 而信号传输单元 5将当时 的计数输出。
上述方案中， 所述计数单元 4采用一个计数器来实现， 该计数器的 数字包含了时间点信息和锯齿波信号的电压大小信息， 用于与信号输出 单元 5输出端连接的计算机进行数据恢复。
上述方案中， 所述信号输出单元 5的激励信号是由信号比较单元 3 产生的脉冲信号，信号输出单元 5输出是由计数单元 4产生的即时数字。
(三） 有益效果
从上述技术方案可以看出， 本发明具有以下有益效果：
1、 本发明提供的随机采样器， 从其结构组成上来看， 不需要存储 单元， 不需要 AD采样器以及不需要传统采样方式的压缩处理单元， 所 以不需要对数据进行存储节省硬件成本和功耗， 硬件复杂度低， 实现了 真正的随机采样， 更加适用于一维缓变信号的采集。
2、 本发明提供的随机采样器， 应用了压缩感知的原理降低了采样 频率， 在可重构原始信号的前提下， 实现了低于奈奎斯特频率的采样。 举例说明如下： 假设一个信号依照奈奎斯特频率采样需要一秒钟采十个 点， 而利用本发明提供的随机采样器进行采样可以控制在一秒钟采两到 三个点， 因为本发明采样的时间点是由锯齿波和输入信号共同决定的， 两个信号作比较每相等一次记录一个点， 也就是说锯齿波的斜率越小采 样频率也就越低， 以此来实现对采样频率的降低。 而压缩感知是一个理 论基础， 低采样率的情况下只有符合压缩感知的要求， 并且通过压缩感 知的重构算法才能重构信号。
3、 本发明提供的随机采样器， 硬件复杂度更低， 低于传统方式和 AIC采样器， 更易于实现， 降低硬件成本的同时降低系统功耗。 4、 本发明提供的随机采样器， 由于不需要进行混频， 而混频会增 加信号的复杂度， 因此更适用于一维缓变信号的采集， 不会增加信号的 复杂度。
5、 本发明提供的随机采样器， 相比较 AIC系统而言， AIC系统的 测量矩阵要知道全部的伪随机序列的值， 然后确定截取其中哪一部分， 才能确定测量矩阵， 而本发明的测量矩阵只要接收到计数器的值就可以 得到， 因此其采样矩阵更容易确定， 进而由其采集的信号更易于应用压 缩感知的方法进行重构。
6、 本发明提供的随机采样器， 输出的是一个计数器产生的计数， 并且不需要先存储后发送， 所以节省了存储空间。
附图说明 为了更进一歩说明本发明的内容， 以下结合附图及实施例子， 对本 发明做详细描述， 其中：
图 1为现有技术中随机采样器的结构示意图；
图 2为依照本发明实施例的适用于一维缓变信号的随机采样器的结 构示意图；
图 3为图 2中信号预处理单元要达到的效果的示意图；
图 4为图 2中斜率可控的锯齿波信号发生单元的结构示意图； 图 5为利用本发明提供的随机采样器随机采样的数据用基于压缩感 知的 OMP算法恢复信号同原始信号的对比及误差。
具体实施方式 为使本发明的目的、 技术方案和优点更加清楚明白， 以下结合具体 实施例， 并参照附图， 对本发明进一歩详细说明。
本发明提供的随机采样器与图 1所示的 AIC采样器从原理上是完全 不同的， 图 1所示的 AIC采样器通过对信号进行混频， 然后再低速采样 的方法实现了信号的随机采样； 而本发明提供的随机采样器是利用两个 信号相比较的交点的随机性来实现信号的随机采样， 由于本发明没有对 信号进行混频， 因此也就没有增加信号的复杂性， 并且上述实现原理的 不同导致了整个硬件实现的完全不同。
如图 2所示， 图 2为依照本发明实施例的适用于一维缓变信号的随 机采样器的结构示意图， 该随机采样器包括信号预处理单元 1、 斜率可 控的锯齿波信号发生单元 2、 信号比较单元 3、 计数单元 4和信号传输 单元 5。 其中， 信号比较单元 3输出的脉冲信号用来控制斜率可控的锯 齿波信号发生单元 2和信号传输单元 5。 下面针对各个部分进行详细介 绍。
1、 信号预处理单元
信号预处理单元 1用于在输入信号到达信号比较单元 3之前对输入 信号进行预处理， 并将预处理后的输入信号传输给信号比较单元 3， 以 在有突变的情况下能够更多地采集数据， 提高平均采样率； 其中该预处 理是对输入信号进行反转处理。 对于接近零的数据随机采样器采集频率 高的特点， 本发明对信号进行预处理， 使其反转从而使随强度增大的信 号能够得到更好采样。 本发明提供的随机采样器在信号接近零处数据采 集频率会增大， 而传感器信号的突变通常是正方向的变化， 实际需求是 在有变化时更多的采集数据， 所以需要对采集的数据进行预处理， 该预 处理主要是对输入信号进行反转， 预期达到的效果如图 3所示， 可以看 到右边的信号是左边的信号的反转。
2、 斜率可控的锯齿波信号发生单元
斜率可控的锯齿波信号发生单元 2用于生成斜率可控的锯齿波信号， 并实现清零处理， 该锯齿波信号被输送给信号比较单元 3， 并在信号比 较单元 3中与经过预处理的输入信号进行比较，在二者相等时输出脉冲， 同时斜率可控的锯齿波发生单元 2清零， 重新产生新的锯齿波信号， 并 重复上述动作， 其目的是使本发明提供的随机采样器自身生成的锯齿波 信号与输入信号进行大小对比， 利用其相等的情况的随机性而产生一个 随机的脉冲， 再利用后面的计数器及信号传输单元将相等的点的特征信 息传到与信号传输单元 5输出端连接的计算机， 然后通过压缩感知理论 的重构算法进行恢复。 其中， 在通过压缩感知理论的重构算法进行恢复 时， 压缩感知理论本质上是在解一个欠定方程 . =〈< 〉， 其中该欠定方 程 . =〈ί 〉的右边 为压缩感知获取的 M个采样值，是采集到的信号组 成的矩阵， 左边是原始信号 J与系数矩阵 的乘积， 系数矩阵 用于对原 始信号进行稀疏及测量。 本发明得到的计数器输出的信号中包含了测量 矩阵的信息和测量值信息， 且稀疏矩阵可以自定义， 所以压缩感知基本 的欠定方程已经构造好了， 目前科学界已经有了比较成熟的解该欠定方 程的算法， 可以直接套用， 具体可以参考下文的常用信号重构算法。 另 外， 由于锯齿波信号和输入信号不断地进行对比，相等时进行一次采样， 锯齿波斜率越小相遇的时间点越靠后， 所以锯齿波信号的斜率决定了随 机采样的平均采样率， 为了适应不同的信号所以要保证锯齿波信号的斜 率是可调的。
如图 4所示为斜率可调的锯齿波发生单元的结构示意图， 其中包括 了一个恒流源、 一个电容和一个由脉冲信号触发的开关。 通过调节恒流 源的电流大小来控制锯齿波信号的斜率， 通过由脉冲触发的开关来对锯 齿波信号电压进行清零。
此处， 对压缩感知理论的重构算法进行简要介绍。 压缩感知是一种 新的信息获取理论， 是建立在信号稀疏表示、 测量矩阵的非相关性以及 逼近理论上的一种信号采集和重建的方法。 该理论指出， 只要信号是稀 疏的或者在某个基下时刻压缩的， 就可以通过远低于奈奎斯特采样定理 要求的采样率获取信号的结构信息， 再通过重构算法完成信号的精确重 构。 压缩感知理论只要包括两个部分： 将信号在观测向量上投影得到观 测值， 以及利用重构算法由观测值重构信号。
设 ^是一个长度为 N的信号， 其稀疏度为 (^ < Λ ， 稀疏度为 指 ^ 本身有 ^个非零元素， 或者在某种变化域 Ψ内的展开系数有 ^个非零元 素。 信号 ^ (假设信号在变换域 Ψ内 ^系数） 在观测向量上的投影可以 表示为： 其中， 为压缩感知获取的 M个采样值， 1=1， … ·Μ，Μ〈Ν,
Figure imgf000009_0001
是一组观 Ψ测向量， 由 组成的观测基 Φ与变换基 Ψ不相关。
ψ
重构信号的关键是找出信号 ^在 Ψ域中的稀疏表示， 可以通过 /。范 数优化问题找到具有系数结构的解：
mm s.t. y - Φχ 由于上式的优化问题是一个难求解的 NP-hard问题，所以可以用 I、约 束取代 /。约束：
mm s.t. γ = Φχ 此时， 压缩感知获得的采样值已经保持了原信号的结构及相关信息， 因此可以不需要重构信号， 利用检测算法直接从采样值中提取特征量进 行判断， 完成信号检测任务。
常用信号重构算法有最小 范数模型、 匹配追踪算法和正交匹配追 踪算法， 其中：
1 ) 最小 范数模型
从数学意义上讲， 基于压缩感知理论的信号重建问题就是寻找欠定 方程组 (程的数量少于待解的未知数)的最简单解的问题， ¾范数刻画得 就是信号中非零元素的个数， 因而能够使得结果尽可能地稀疏。 通常我 们采用下式描述最小 4范数最优化问题：
Figure imgf000009_0002
实际中， 允许一定程度的误差存在， 因此将原始的最优化问题转化 成一个较简单的近似形式求解， 其中 是一个极小的常量：
in l s.t. |F— Φ | ≤ (3.2)
但是这类问题的求解数值计算极不稳定， 很难直接求解。
匹配追踪类稀疏重建算法解决的是最小 范数问题， 最早提出的有 匹配追踪 (MP)算法和正交匹配追踪 (ΟΜΡ)算法。
2) 匹配追踪算法
匹配追踪算法的基本思想是在每一次的迭代过程中， 从过完备原子 库里 (即感知矩阵：)选择与信号最匹配的原子来进行稀疏逼近并求出余量, 然后继续选出与信号余量最为匹配的原子。 经过数次迭代， 该信号便可 以由一些原子线性表示。但是由于信号在己选定原子 (感知矩阵的列向量) 集合上的投影的非正交性使得每次迭代的结果可能是次最优的， 因此为 获得较好的收敛效果往往需要经过较多的迭代次数。
匹配追踪类算法通过求余量 r与感知矩阵 Φ中各个原子之间内积的 绝对值， 来计算相关系数 u:
U
Figure imgf000010_0001
'， X;- , N
并采用最小二乘法进行信号逼近以及余量更新：
Λ = arg Ι-Λ'Λ If - Φ·-, * «··'
ί€ 1 **;
= - Φ,Χ
3 ) 正交匹配追踪算法
正交匹配追踪算法 （Orthogonal Matching Pursuit,OMP ) , 是最早的 贪婪迭代算法之一。 该算法沿用了匹配追踪算法中的原子选择准则， 只 是通过递归对己选择原子集合进行正交化以保证迭代的最优性， 从而减 少迭代次数。 ΟΜΡ算法则有效克服了匹配追踪算法为获得较好的收敛效 果往往需要经过较多的迭代次数的问题。
ΟΜΡ算法将所选原子利用 Gram-Schmidt正交化方法进行正交处理 再将信号在这些正交原子构成的空间上投影， 得到信号在各个已选原子 上的分量和余量， 然后用相同方法分解余量。 在每一歩分解中， 所选原 子均满足一定条件， 因此余量随着分解过程迅速减小。 通过递归地对已 选择原子集合进行正交化保证了迭代的最优性， 从而减少了迭代次数。
OMP的重建算法是在给定迭代次数的条件下重建，这种强制迭代过 程停止的方法使得 OMP需要非常多的线性测量来保证精确重建。总之， 它以贪婪迭代的方法选择 Φ的列， 使得在每次迭代中所选择的列与当前 的冗余向量最大程度地相关， 从测量向量中减去相关部分并反复迭代， 直到迭代次数达到稀疏度 ， 强制迭代停止。
OMP算法的具体歩骤如下：
(1)初始余量 = 迭代次数《- 1， 索引值集合 A = 0， / - 0； (2；)计算相关系数 u ， 并将 u中最大值对应的索引值存入 /中；
(3)更新支撑集 ， 其中 A = A U /e ;
(4)应用式 (3.3)得到 i， 同时用式 (3.4)对余量进行更新；
(5) 若 I ew— r|| ≥ ε2， 令 = 7^ ， η=η+ \ , 转歩骤 （2 ) ; 否则， 停止迭代。
3、 信号比较单元
信号比较单元 3用于将信号预处理单元 1输入的输入信号与斜率可 控的锯齿波发生单元 2生成的锯齿波信号进行比较， 在二者相同时输出 脉冲信号给斜率可控的锯齿波发生单元 2和信号传输单元 5， 用于斜率 可控的锯齿波发生单元 2的清零及信号传输单元 5的处理。 信号比较单 元 3 是本发明提供的随机采样器中硬件实现最简单却是最核心的部分， 本发明主要是利用斜率可控的锯齿波发生单元 2生成的锯齿波信号与输 入信号的比较实现随机脉冲信号的生成， 从而实现了真正意义上的随机 采样。
信号比较单元 3主要由一个比较器构成， 斜率可控的锯齿波发生单 元 2生成的锯齿波信号与经过信号预处理单元 1预处理后的输入信号分 别从比较器正输入端和负输入端输入， 当锯齿波信号小于输入信号时， 比较器的输出端为低电平， 当锯齿波信号等于输入信号或者大于输入信 号时， 比较器的输出端为高电平， 此时锯齿波信号发生单元被清零开始 新一次的锯齿波信号生成。 同时信号传输单元 5将当时的计数输出给计 算机。
4、 计数单元
计数单元 4用于在锯齿波信号发生单元 2生成锯齿波信号的同时对 时钟信号开始计数， 并传输给信号输出单元 5 ; 该计数单元 4一般是采 用一个计数器来实现， 由于锯齿波信号的斜率已知， 所以这个计数器的 数字包含了时间点信息和锯齿波信号的电压大小信息。 计数器的数字包 含了两个主要信息， 用于计算机端进行数据恢复。 此处的时钟信号的频 率可以调节， 以保证最终信号的恢复。
5、 信号输出单元 信号输出单元 5用于在接收到信号比较单元 3输出的脉冲信号后输 出计数单元 4当时计数的数字给计算机， 该计算机连接于信号输出单元 5。 信号传输单元 5的激励信号是由信号比较单元 3产生的脉冲信号， 输出的内容是由计数单元 4产生的即时数字。
利用本发明提供的适用于一维缓变信号的随机采样器， 通过采用随 机采样的方法对气体传感器的信号进行采集和恢复的仿真可以发现， 随 机采样的方法是在一定误差允许的范围内可行的， 如图 5所示随机采样 的信号恢复情况对比图。
从上述实施例可以看出， 从原理上来看， 本发明提供的随机采样器 真正实现了信号在时域的随机采集， 同时有了真正的随机性， 因为图 1 所示的 AIC采样器混频用的是伪随机序列， 并不是真正的随机混频。从 电路上来看， 本发明提供的随机采样器整个硬件电路没有存储器部分， 没有伪随机序列发生器部分， 没有 ADC芯片， 电路更加简单， 容易实 现， 节省了存储空间和功耗。
以上所述的具体实施例， 对本发明的目的、 技术方案和有益效果进 行了进一歩详细说明， 所应理解的是， 以上所述仅为本发明的具体实施 例而已， 并不用于限制本发明， 凡在本发明的精神和原则之内， 所做的 任何修改、 等同替换、 改进等， 均应包含在本发明的保护范围之内。

Claims

权利要求
1、 一种适用于一维缓变信号的随机采样器， 其特征在于， 该随机 采样器包括信号预处理单元（ 1 )、斜率可控的锯齿波信号发生单元（2)、 信号比较单元 （3 )、 计数单元 （4) 和信号传输单元 （5)， 其中：
信号预处理单元 （1 )， 用于对输入信号进行预处理， 并将预处理后 的输入信号传输给信号比较单元 （3 );
斜率可控的锯齿波信号发生单元 （2)， 用于生成斜率可控的锯齿波 信号， 并实现清零处理， 该锯齿波信号被输送给信号比较单元 （3 ); 信号比较单元 （3 )， 用于将信号预处理单元 （1 ) 输入的输入信号 与斜率可控的锯齿波发生单元 （2) 生成的锯齿波信号进行比较， 在二 者相同时输出脉冲信号给斜率可控的锯齿波发生单元 （2) 和信号传输 单元 (5)；
计数单元 （4)， 用于在锯齿波信号发生单元 （2) 生成锯齿波信号 的同时对时钟信号开始计数， 并传输给信号输出单元 （5 );
信号输出单元 （5 )， 用于在接收到信号比较单元 （3 ) 输出的脉冲 信号后输出计数单元 （4) 当时计数的数字。
2、 根据权利要求 1 所述的适用于一维缓变信号的随机采样器， 其 特征在于， 所述信号预处理单元 （1 ) 对输入信号进行预处理， 是对输 入信号进行反转处理， 以在有突变的情况下能够更多地采集数据， 提高 平均采样率。
3、 根据权利要求 1 所述的随机采样器， 其特征在于， 所述斜率可 控的锯齿波信号发生单元 （2) 生成的锯齿波信号被输送给信号比较单 元 （3 )， 在信号比较单元 （3 ) 中与经过预处理的输入信号进行比较， 在二者相等时信号比较单元 （3 ) 输出脉冲信号给斜率可控的锯齿波信 号发生单元 （2)， 斜率可控的锯齿波发生单元 （2) 清零， 重新产生新 的锯齿波信号。
4、 根据权利要求 3 所述的随机采样器， 其特征在于， 所述斜率可 调的锯齿波发生单元 （2) 包括一个恒流源、 一个电容和一个由脉冲信 号触发的开关， 通过调节恒流源的电流大小来控制锯齿波信号的斜率， 通过由脉冲触发的开关来对锯齿波信号电压进行清零。
5、 根据权利要求 1 所述的随机采样器， 其特征在于， 所述信号比 较单元 （3 ) 由一个比较器构成， 斜率可控的锯齿波发生单元 （2) 生成 的锯齿波信号与经过信号预处理单元 （1 ) 预处理后的输入信号分别从 比较器正输入端和负输入端输入， 当锯齿波信号小于输入信号时， 该比 较器的输出端为低电平， 当锯齿波信号等于输入信号或者大于输入信号 时， 该比较器的输出端为高电平， 输出脉冲信号给斜率可控的锯齿波发 生单元 （2) 和信号传输单元 （5 )， 斜率可控的锯齿波发生单元 （2) 被 清零开始新一次的锯齿波信号生成， 而信号传输单元 （5 ) 将当时的计 数输出。
6、 根据权利要求 1 所述的随机采样器， 其特征在于， 所述计数单 元 （4) 采用一个计数器来实现， 该计数器的数字包含了时间点信息和 锯齿波信号的电压大小信息， 用于与信号输出单元 （5 ) 输出端连接的 计算机进行数据恢复。
7、 根据权利要求 1 所述的随机采样器， 其特征在于， 所述信号输 出单元 （5) 的激励信号是由信号比较单元 （3 ) 产生的脉冲信号， 信号 输出单元 （5) 输出是由计数单元 （4) 产生的即时数字。
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