CN104771148A - 一种基于小波分解与重构的脉搏波提取方法和采集*** - Google Patents

一种基于小波分解与重构的脉搏波提取方法和采集*** Download PDF

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CN104771148A
CN104771148A CN201510232056.4A CN201510232056A CN104771148A CN 104771148 A CN104771148 A CN 104771148A CN 201510232056 A CN201510232056 A CN 201510232056A CN 104771148 A CN104771148 A CN 104771148A
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Abstract

本发明提出一种基于小波分解与重构的实现人体脉搏波采样信号中直流分量和交流分量分离的方法及脉搏信号采集***,该***通过设定采样频率在100Hz~200Hz的范围内,自动选择小波分解和重构的层数,首先将原始采样数据序列中的直流分量分离出来,并取直流分量序列进行算术平均值作为幅值恒定的直流信号,以此直流信号从原始采样数据序列中分离出幅值和相位均较稳定的交流信号(脉搏波),供血压计算、血氧监测、血流动力PWV监测等应用使用。

Description

一种基于小波分解与重构的脉搏波提取方法和采集***
技术领域
本发明涉及脉搏信号提取的电子信息技术领域,特别是涉及一种利用小波分析,从采样数据中提取脉搏波信号的方法,可以较方便地在单片机(如ARM7)上实现。
背景技术
在医疗电子领域,很多场合需要从传感器的采样数据中分离和提取出人体的脉搏波信号,典型的应用如下:
(1)基于“示波法”的无创血压测量,用于从压力传感器的采样数据中分离和提取脉搏波信号,以便形成脉搏波信号的包络曲线,进行血压计算;
(2)基于光电容积描记(PPG)法的无创血氧测量或PWV监测,从血氧传感器的采样数据中分离和提取光电容积脉搏波,把采样数据分成两部分:直流分量和交流分量,其中交流分量就是PPG脉搏波。
通常从传感器的采样数据中分离和提取所需的脉搏波的方法有两种,这两种方法的基本思路都是先求出采样数据中的直流分量,然后用每个采样点的值减去直流分量,得到交流分量。
第一种方法:考虑到脉搏信号的波形特征是一个周期性的交流信号,在数据采样阶段,可以把传感器的采样时间设定较长,以便能够采集多个脉搏波,但是难以控制传感器的采样时间窗口长度正好是脉搏波周期的整数倍。假设脉搏波每个周期对应的采样数据是R个,一次采样的数据有N个,那么可能形成的等式为:N = R*s + k,其中s是采样到的脉搏波的个数,0≤k≤R。当s足够大时,即使k值不为0或R,计算出N个采样点的算术平均值,作为直流分量,显然这个直流分量存在一定的误差,然后用采样数据减去直流分量,就得到了交流分量。一方面计算出来的直流分量存在一定的误差,这个误差将导致交流分量的计算不准确,因为交流分量的幅度通常只有直流分量幅度的0.5‰左右,因而直流分量中很小的误差,经过运算以后反映到交流分量上就是一个很大的误差;另一方面欲减小直流分量的计算误差,必须加大采样时间,这在很多应用场合是不允许的,例如上述“示波法”的血压测量,当连续采样多个脉搏波时,此时的袖带压力值下降很大,若基于这一组采样数据进行直流信号的处理,则实时性将变差,导致直流分量计算不准确,从而也不能获得准确的交流分量。基于这两方面的考虑,这种方法不太可能取得理想的效果。
第二种方法:采用FFT的方法,把采样到的数据序列x(n)变换到频域X(k),然后仅保留频域序列的X(0)值,序列的其他值全部清0,形成一个新的序列X1,最后对新的频域序列X1做FFT反变换,得到一个新的时域的数据序列x1,那么x1就是采样数据包含的直流分量。采样数据序列x减去其直流分量序列x1,就得到了交流分量。这种方法适合于采样样本数据中直流分量幅度值比较恒定的情况,这使得该方法的使用有很大的局限性,例如,若采样数据的直流分量的幅度不是一个恒定值,而是随时间的变化而变大或变小,那么这样的直流分量经过FFT变换到频域时,将包含丰富的谐波,从而使直流分量的分离变得十分困难,同时获取交流分量也将变得十分困难。
针对上述两种方法的局限性和不足,本发明提出了一种基于小波分解与重构,用于分离和提取采样数据中的直流分量的方法和脉搏波的数据采集***,可以克服以上不足。同时,在完成采样信号数据的小波分解的步骤以后,可以在小波域根据需要进行去噪处理,最后进行小波重构输出所真实的信号。小波分解、去噪、重构的处理过程,充分体现了小波分析方法的优越性。
小波的分解与重构过程需要四个FIR滤波器f1,f2,f3,f4,它们分别为:
LO_D(低通分解滤波器f1)
HI_D(高通分解滤波器f2)
LO_R(低通重构滤波器f3)
HI_R(高通重构滤波器f4)。
假设输入信号序列x(n)的长度为N,其频谱带宽的宽度为B0。低通分解滤波器f1是一个半带低通的FIR滤波器,当它作用于输入信号序列x(n)时,将滤除信号中超过B0/2的所有频率分量;高通分解滤波器f2也是一个半带高通的FIR滤波器,当它作用于输入信号序列x(n)时,将滤除信号中低于B0/2的所有频率分量。
假设采样的数据序列为x,那么对该序列进行离散小波分解的步骤为:首先将序列x与滤波器f1进行卷积运算并下采样(down sampling),输出结果为序列x的近似分量a1,由于下采样使得序列a1的长度为序列x长度的一半。接着将序列x与滤波器f2进行卷积运算并下采样,输出结果为序列x的细节分量d1,同样地因下采样使得序列d1的长度为序列x长度的一半。此时信号序列a1和d1在小波域,可以根据需要进行去噪处理,即小波去噪。小波重构是分解的逆过程,先用序列a1上采样后的新序列(长度是a1的2倍)与滤波器f3进行卷积,输出重构的低频分量,接着用序列d1上采样后的新序列(长度是的d1的2倍)与滤波器f4进行卷积,输出重构的高频分量,最后将重构的低频分量序列与重构的高频分量序列相加,即得到重构后的序列,理论上其波形和相位信息应与输入的序列x相同。
如果继续对序列a1进行小波分解,其输出的近似分量和细节分量的序列分别为a2、d2,注意序列a2、d2的长度均减小为上一层序列a1或d1长度的一半。同样地,若继续分解到第j层,输出的近似分量和细节分量的序列分别为aj、dj,注意序列aj、dj的长度均减小为上一层近似分量序列或细节分量序列长度的一半。
表1列出了一个进行8层小波分解的过程以及每层小波分解的输入和输出序列及其长度。
表1
参考文献:
1、瞿浩正(发明人),《一种在电子血压计中确定收缩压和舒张压的算法》,中国发明专利号ZL 2013101292426,状态:已授权。
2、刘娜,《基于脉搏波的血压和心血管状态检测算法研究》,浙江大学硕士论文,2004年
3、高博,《脉搏血氧饱和度检测仪的研制》,百度文库。
发明内容
为了克服上述现有技术的不足,本发明提出了一种基于小波分解与重构,用于分离和提取采样数据中的直流分量的方法和脉搏波的数据采集***。本发明所采用的技术方法的原理在于:
1. 正确认识人体脉搏波的信号特征
人体脉搏波信号的能量分布在0.2Hz~45Hz的频带内,而在0.2Hz~10Hz内分布了95%以上的能量,因此可以认为人体脉搏信号的功率谱密度频带范围为0.2Hz~45Hz。对于这样特征的信号,进行采样时,设定采样频率在100Hz~200Hz的范围内取值,从下面采用的小波分解的方法将会看到,100Hz~200Hz的采样频率是一个合理的值。其次,根据Nyquist采样定理,采样频率应大于信号频谱中最高频率的2倍,则理论上设定的采样频率应大于90Hz,如100Hz、200Hz、300Hz、……。反过来考虑,如果设定的采样频率为M,则意味着采样数据的频谱中允许存在的最高频率为M/2,若M值过高,显然采样到的数据序列在45~M/2的频带内可能混入噪声或干扰,为了滤除采样引入的噪声或干扰,需要单独的开销对其进行处理。所以不应将采样频率设置过高。
2. 小波多分辨率的分析
对原始采样的序列x进行多分辨率的小波分析,就是根据信号处理的实际需要,进行多层的小波分解。根据小波分解的原理,下一层的小波分解是针对上层的小波近似分量进行的,每完成一层的小波分解,输出的下层近似分量的频带宽度是上层近似分量频带宽度的一半,因此当小波分解进行到一定的层次时,此时输出的小波域的近似分量将只对应着原始采样数据信号中的直流分量,将该层的近似分量进行小波重构,重构恢复出来的信号就是原始采样数据中的直流分量。因此在进行每一层的小波分解时,只需要将低通分解滤波器f1(LO_D)作用于输入序列便可。
根据前面对人体脉搏波信号特征的认识和了解,其频谱范围大致在0.2Hz~45Hz之间,而采样频率设定为100Hz,那么采样数据包含的实际频谱范围为0~50Hz,因此采样数据中完全包含了脉搏波。假设进行了j层的小波分解,在j层输出的近似分量的频带宽度为0.2Hz,那么此时j层小波域的近似分量不包含有脉搏波信号的小波分量,只包含直流分量的小波分量,此时的直流分量近似于一个幅值恒定的直流信号。小波分解到j层以后,无需在进一步做小波分解。j应满足下列数学公式:,由此计算j为:
,ceil(c)表示取大于或等于浮点数c的最小整数 ……………………..….(式1)
可见当采样频率较低时,小波分解的层数也少。例如***设定采样频率为100Hz,代入(式1),计算出j≈8,即小波分解进行到第8层时,输出的近似分量序列a8与原始采样数据中低于0.2Hz的频率成份对应。而当采样频率设置为200Hz时,根据(式1)计算出来的小波分解层数j≈9。
假设原始采样数据序列x(n)的长度为N,用一维向量可以表示为:
x = [x1,x2,x3,…,xN]
根据前面的知识,当向量x进行8层小波分解时,在第8层输出长度为L8的近似分量序列a8表示为:
a8 = [r1,r2,r3,…,rL8]
3. 脉搏波信号中直流分量的分离
在输入的原始采样数据序列x(n)的多分辨率分解过程中,求出了在最终的分解层数j的近似分量aj,小波域的aj对应着原始采样数据序列x(n)中低于0.2Hz的频率成份,所以只需对小波域的aj序列进行小波重构,恢复到时域的序列为z(n),其长度与原始采样数据序列x(n)相同。显然序列z(n)就是原始数据序列x(n)中包含的直流分量(及其谐波),对序列z(n)求算术平均值,就是原始数据序列x(n)中的直流分量。
例如,对小波域的a8 = [r1,r2,r3,…,rL8]进行小波重构,将使用到低通重构滤波器f3和高通重构滤波器f4,因为目的是重构第8层的小波域近似分量,所以在重构时应将每一层的细节分量用0代替。重构步骤:
首先将小波域的近似分量a8进行上采样(up sampling),得到一个新的序列:
a8_u = [r1,0,r2,0,r3,0…,rL8,0],序列长度增加一倍,为2*L8
接着将低通重构滤波器f3作用于序列a8_u,得到重构在第7层得到一个长度为L7的近似分量序列a7_r。
重复重构过程,将序列a7_r上采样后得到一个长度为2*L7的序列a7_u,继续将低通重构滤波器f3作用于序列a7_u,……,直至在第1层得到一个输出序列a1_r,它就是上面所说的恢复到时域的序列z(n),其长度与原始采样数据序列相同,可以用一维向量表示为:
z = [z1,z2,z3,…,zN]
表示向量z的算术平均值,则
最后得到原始采样数据序列中包含的:
直流分量为
交流分量为x = [(x1-),(x2-),(x3-),…,(xN-)]。
通过本发明的技术方案处理的交流信号,是一个幅度和相位均较稳定的交流信号。便于血压值、血氧饱和度的计算或进行PWV的监测。
4. 小波基的选择
本发明技术方案在计算和确定采样数据序列x中的直流分量过程中,可以选择多种小波基,如haar小波、db4小波、以及双正交样条小波bior(Nr.Nd)等。用不同的小波基,计算出来的直流分量的算术平均值,其误差在万分之一的范围内。为计算方便,建议选择的haar或db4小波基。
本发明所采用的人体脉搏波数据采集***的原理框图如图1和图2所示。
该***包含一个传感器与采样电路的模块、一个采样频率控制模块、一个小波分解与重构模块以及一个直流分量和交流分量分离的模块。
采样频率控制模块可以在100Hz~200Hz的范围内选择采样频率,并根据采样频率的取值自动设定小波分解的层数,当采样频率为100Hz~150Hz的范围内时,将小波分解层数设定为8,当采样频率为150Hz~200Hz时,将小波分解的层数设定为9。
小波分解与重构模块,则根据采样频率控制模块给出的分解层数,将输入的采样信号序列x,按需要进行设定层数的小波分解,并将最下层的近似分量进行重构,输出采样信号中的直流分量信号序列z。
直流分量和交流分量分离模块,实现采样信号序列x中的直流分量和交流分量的分离,输出采样信号中的交流分量序列,这个交流分量序列就是我们需要的脉搏波信号,是一个幅度和相位均较稳定的交流信号。
附图说明
图1为采样频率为100Hz时的人体脉搏波数据采集***原理图(注意图中对功能框的图例说明);
图2为一组实际的采样数据(fs=100Hz)的信号序列x的波形;
图3为经过8层小波分解后的近似分量a8重构出来的直流分量波形图;
图4为分离直流信号后的交流信号波形图。
具体实施方式
本发明以一组实际的血氧探头采集到的原始数据为例,通过MATLAB软件提供的函数功能和命令,来分析如何如何通过小波分解和重构达到从原始数据中提取和分量直流分量和交流分量的目的。
以下为MATLAB的程序:
%准备原始采样数据序列x,长度为512,传感器电路的采样频率为100Hz.
x=[0.567664,0.567814,0.567983,0.568176,0.568390,0.568623,0.568869,0.569116,0.569350,0.569553,0.569706,0.569788,0.569778,0.569655,0.569403,0.569007,0.568461,0.567763,0.566916,0.565933,0.564831,0.563635,0.562371,0.561072,0.559772,0.558502,0.557296,0.556182,0.555185,0.554325,0.553617,0.553071,0.552689,0.552472,0.552414,0.552506,0.552738,0.553097,0.553567,0.554134,0.554783,0.555497,0.556260,0.557056,0.557866,0.558673,0.559461,0.560208,0.560901,0.561522,0.562059,0.562499,0.562839,0.563074,0.563206,0.563244,0.563200,0.563087,0.562926,0.562734,0.562533,0.562341,0.562175,0.562049,0.561970,0.561947,0.561977,0.562061,0.562191,0.562361,0.562558,0.562775,0.563002,0.563231,0.563455,0.563669,0.563873,0.564064,0.564244,0.564413,0.564576,0.564736,0.564894,0.565056,0.565220,0.565387,0.565559,0.565734,0.565909,0.566085,0.566256,0.566421,0.566577,0.566725,0.566862,0.566990,0.567112,0.567229,0.567348,0.567474,0.567611,0.567764,0.567938,0.568136,0.568356,0.568595,0.568846,0.569098,0.569335,0.569541,0.569698,0.569781,0.569771,0.569649,0.569397,0.569002,0.568459,0.567764,0.566923,0.565948,0.564856,0.563670,0.562418,0.561129,0.559836,0.558571,0.557365,0.556246,0.555237,0.554361,0.553632,0.553059,0.552650,0.552407,0.552324,0.552398,0.552621,0.552979,0.553462,0.554055,0.554741,0.555505,0.556327,0.557189,0.558070,0.558947,0.559798,0.560603,0.561341,0.561993,0.562544,0.562985,0.563306,0.563510,0.563599,0.563585,0.563482,0.563307,0.563085,0.562836,0.562584,0.562348,0.562147,0.561995,0.561900,0.561866,0.561896,0.561981,0.562119,0.562298,0.562509,0.562738,0.562978,0.563220,0.563455,0.563680,0.563892,0.564089,0.564273,0.564446,0.564610,0.564768,0.564924,0.565079,0.565237,0.565397,0.565562,0.565731,0.565900,0.566070,0.566239,0.566403,0.566560,0.566710,0.566851,0.566982,0.567108,0.567228,0.567348,0.567475,0.567611,0.567763,0.567934,0.568129,0.568346,0.568583,0.568834,0.569087,0.569329,0.569545,0.569712,0.569810,0.569817,0.569713,0.569479,0.569103,0.568574,0.567891,0.567057,0.566084,0.564987,0.563793,0.562527,0.561221,0.559911,0.558627,0.557404,0.556271,0.555254,0.554374,0.553646,0.553081,0.552682,0.552450,0.552380,0.552463,0.552687,0.553040,0.553508,0.554075,0.554725,0.555442,0.556209,0.557009,0.557824,0.558637,0.559429,0.560183,0.560880,0.561506,0.562045,0.562488,0.562829,0.563063,0.563195,0.563231,0.563183,0.563066,0.562899,0.562702,0.562496,0.562299,0.562129,0.561999,0.561918,0.561891,0.561922,0.562005,0.562134,0.562302,0.562498,0.562715,0.562940,0.563167,0.563391,0.563604,0.563808,0.564000,0.564181,0.564356,0.564525,0.564693,0.564862,0.565034,0.565210,0.565389,0.565573,0.565757,0.565940,0.566119,0.566292,0.566454,0.566604,0.566741,0.566864,0.566975,0.567078,0.567177,0.567277,0.567385,0.567508,0.567650,0.567818,0.568012,0.568235,0.568481,0.568742,0.569008,0.569262,0.569486,0.569660,0.569760,0.569765,0.569654,0.569410,0.569019,0.568477,0.567778,0.566931,0.565949,0.564848,0.563655,0.562397,0.561107,0.559818,0.558562,0.557370,0.556270,0.555286,0.554436,0.553735,0.553190,0.552804,0.552577,0.552504,0.552577,0.552786,0.553119,0.553564,0.554107,0.554734,0.555430,0.556179,0.556966,0.557774,0.558583,0.559376,0.560135,0.560841,0.561476,0.562028,0.562485,0.562838,0.563085,0.563228,0.563273,0.563233,0.563122,0.562959,0.562764,0.562557,0.562357,0.562180,0.562042,0.561954,0.561919,0.561940,0.562016,0.562140,0.562306,0.562502,0.562723,0.562955,0.563192,0.563427,0.563653,0.563869,0.564071,0.564262,0.564441,0.564613,0.564778,0.564940,0.565101,0.565266,0.565433,0.565604,0.565779,0.565955,0.566134,0.566309,0.566480,0.566645,0.566801,0.566947,0.567081,0.567207,0.567325,0.567440,0.567557,0.567679,0.567814,0.567964,0.568134,0.568325,0.568534,0.568757,0.568985,0.569205,0.569402,0.569556,0.569647,0.569655,0.569558,0.569340,0.568984,0.568482,0.567828,0.567026,0.566086,0.565020,0.563853,0.562609,0.561320,0.560019,0.558738,0.557511,0.556366,0.555333,0.554433,0.553681,0.553092,0.552669,0.552414,0.552323,0.552388,0.552599,0.552943,0.553405,0.553970,0.554621,0.555341,0.556112,0.556919,0.557741,0.558561,0.559361,0.560121,0.560824,0.561455,0.561999,0.562446,0.562789,0.563025,0.563157,0.563193,0.563144,0.563025,0.562855,0.562656,0.562446,0.562246,0.562074,0.561944,0.561863,0.561838,0.561873,0.561962,0.562100,0.562278,0.562486,0.562716,0.562954,0.563195,0.563431,0.563656,0.563869,0.564070,0.564258,0.564436,0.564607,0.564773,0.564938,0.565104,0.565274,0.565446,0.565622,0.565799,0.565976,0.566151,0.566319,0.566482,0.566632,0.566773,0.566902,0.567019,0.567128,0.567232,0.567335,0.567445,0.567566,0.567703,0.567863,0.568047,0.568255,0.568487,0.568733,0.568984,0.569225,0.569440,0.569608,0.569708];
%对序列x进行小波分解,选择小波基为’db4’,分解层数为8,波形见图2
[c,l]=wavedec(x,8,'db4');
%将第8层的近似分量,进行小波重构,恢复为时域的序列z,波形见图3
z=wrcoef('a',c,l,'db4',8);
%原始采样数据中的直流分量
mean(z);
%原始采样数据中的交流分量,波形见图4
x-mean(z).*ones(1,512)。

Claims (8)

1.一种基于小波分解与重构的人体脉搏波采集***,实现对人体的脉搏信号的采集和处理,其特征是:脉搏波采集***由一个传感器与采样电路模块、一个采样频率控制模块、一个小波分解与重构模块以及一个直流分量和交流分量分离模块共四个模块组成,该***的采样频率                                                取值范围为100Hz<=<=200Hz。
2.一种基于小波分解与重构的人体脉搏波信号提取方法,实现对输入的原始采样数据序列中的直流分量和交流分量的分离,其特征是:对输入信号序列x进行多分辨率的小波分析,计算小波分解的层数j的公式为,其中ceil(c)表示取大于或等于浮点数c的最小整数,为脉搏波采集***设定的采样频率。
3.根据权利要求2所述的方法,其特征是:当脉搏波采集***设定的采样频率为 =100Hz时,小波分解的层数为8,当采样频率满足100Hz<<=200Hz时,小波分解的层数为9,小波分解与重构模块按设定的层数j=8或j=9进行小波分解与重构。
4.根据权利要求2所述的方法,其特征是:对输入信号序列x进行多分辨率的小波分析,实现求取序列x中直流分量,在小波分解过程中只使用低通分解滤波器而不使用高通分解滤波器,在小波重构过程中只使用低通重构滤波器而不使用高通重构滤波器。
5.根据权利要求2所述的方法,其特征是:通过小波分解和重构的方法,得到的输入信号序列中包含的直流分量的序列z,以序列z的算术平均值作为输入信号序列中的幅值稳定的直流信号。
6.根据权利要求1所述的***,其特征是:根据***的采样频率控制模块设定的不同采样频率,小波分解与重构模块具有自动选择相应的分解层数的功能,选择的依据是权利要求2中的小波分解层数计算公式。
7.根据权利要求2所述的方法,其特征是:小波分解与重构模块首先提取出输入序列x中的直流信号,然后经过直流分量和交流分量分离的模块处理,输出的交流分量是一个幅度稳定的脉搏波交流信号。
8.根据权利要求1所述的***,其特征是:该***若用于分离原始采样数据序列中的直流信号和交流信号,则其小波分解与重构模块的中只需要包含低通分解滤波器和低通重构滤波器,不需要高通分解滤波器和高通重构滤波器。
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