Question

我有两个嘈杂的信号：

vv = 

130.004701157424    0.0324551387935370  -0.00451469350442727
130.011647685172    0.0293209698881577  -0.00443672007848742
130.018593981487    0.0174427299727758  -0.00604150583046056
130.025540509235    0.00932950167238858 -0.00674349719282885
130.032484953732    0.00662683499867775 -0.00652548843970368
130.039431597197    0.00963962170597527 -0.00271561211198806
130.046378009228    0.00916636267883020 -0.00458483912768415
130.053323495409    0.00848153573266126 -0.00542464163811399
130.060270138874    0.0104189382416956  -0.00464131395425218
130.067215277788    0.00953497010962494 -0.00598548927183946
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130.108893402826    0.0106008069840205  0.00186444703878395
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130.671541550869    0.0170153994249751  0.00376972837524243
130.678487615750    0.0259979013326192  0.00613225792836833
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131.928804976840    0.0626818284978336  0.000282063156230429
131.935752430556    0.0635464647057962  0.000580274100755748
131.942699537005    0.0566494388730308  0.00431660946708819
131.949646643570    0.0583525411330150  0.00277525764449119
131.956592013917    0.0596529719736909  0.00493360735378987
131.963538888932    0.0610801327966719  0.00343154478076365
131.970485763831    0.0631608078188618  0.00207255618093954
131.977432754680    0.0599516632575944  0.00172334574260520
131.984380092562    0.0598524038736555  0.00429462031922425
131.991327199128    0.0567873735033396  0.00123769683953092
131.998274189860    0.0538338332361625  0.00198994909017887
132.005221064759    0.0550579551158673  -0.00249959734021306
132.012167361073    0.0513248026494203  -0.00122223260656512
132.019111921286    0.0491895154110539  -0.00180010672543284
132.026056828650    0.0476692357284076  -0.00476450974438637
132.032998495360    0.0524899258214720  -0.00475888809953603
132.039943287007    0.0500982073998819  -0.00555833539140166
132.046888078653    0.0522093648368018  -0.00660130469926532
132.053832175883    0.0499191108638875  -0.00771434016901260
132.060776736096    0.0535031956712866  -0.00733786776070131
132.067719444490    0.0555732983026725  -0.00822099892651191
132.074665277821    0.0560626959851276  -0.00611423395938753
132.081607175965    0.0522720025083649  -0.00949864547015161
132.088552199045    0.0460141727021084  -0.0111864004085499
132.095497800943    0.0456659392245141  -0.00871128395314326
132.102443055573    0.0433286927215380  -0.0107623349828017
132.109386921252    0.0419849745397525  -0.00801739990674093
132.116329629647    0.0387390188634245  -0.0107573515089166
132.123275347261    0.0330727751424722  -0.0150569553020259
132.130220717608    0.0318127443263756  -0.0127272723348182
132.137166203672    0.0364567670450558  -0.0128709276252399
132.144109375051    0.0342287121069688  -0.0119896103757337
132.151054629681    0.0297918019223798  -0.00897914169021081
132.157999884311    0.0296256037886811  -0.0126487854216226
132.164945717642    0.0360290821093720  -0.00801020601982271
132.171890740723    0.0403938174748625  -0.00705915996178831
132.178836342620    0.0353021767827033  -0.00735206089326397
132.185779629599    0.0331795996056022  -0.0100213235631181
132.192725115779    0.0331569058696126  -0.00769504149961907
132.199670254576    0.0414409707000433  -0.00979003314090525
132.206615740757    0.0419021773926508  -0.00670772042685770
132.213561458371    0.0375111015969745  -0.00575890297225611
132.220507060152    0.0337352238165512  -0.00751052061730450
132.227453356466    0.0285397639189766  -0.00771402657163913
132.234397222262    0.0325982663895901  -0.00732173094862477
132.241343518460    0.0277308387294906  -0.0119691716795284
132.248288425940    0.0218910146898687  -0.00696870032603571
132.255234837972    0.0211966534869462  -0.00817345784534812
132.262181018570    0.0247869588376762  -0.00984313802684687
132.269127430601    0.0270024807721633  -0.00778388333983148
132.276073263932    0.0256695309425160  -0.0123254734426166
132.283018287013    0.0263989215368988  -0.00785086317462576
132.289964930594    0.0259620568447301  -0.0113905764832590
132.296910185225    0.0209857975644172  -0.00700874702672643
132.303855208305    0.0215751228686248  -0.00432029366027902
132.310800231502    0.0223669196947528  -0.00815668089673350
132.317746759250    0.0228319289448673  -0.00912167858220261
132.324692245314    0.0216307542625950  -0.00713917029470587
132.331638657462    0.0135028453915764  -0.00277651187195760
132.338585416644    0.00813390381829617 -0.00339156231002729
132.345532175943    0.0135096298509657  -0.00555915723450343
132.352478819408    0.0148582193704977  -0.00532521352475677
132.359423148187    0.0185929605425803  -0.00498162030696373
132.366368634251    0.0191984097086291  -0.00267056555763903
132.373315277833    0.0179767799398566  -0.000709246696449680
132.380261805581    0.0182765396118518  -0.00175696059383416
132.387206828661    0.0195270150964356  -0.00760521397608591
132.394151851858    0.0190134494656363  -0.00423139300074821
132.401097800906    0.0179654813687979  -0.000831554941118412
132.408044560204    0.0119242568063669  -0.00256134253015786
132.414990972236    0.0164268827087314  -0.00292530923495597
132.421937268551    0.0180304514957133  -0.00839390541281580
132.428883912016    0.0184064573515405  -0.00664066030639073

其中第一列是十进制日的时间，第二列和第三列是两个信号。此数据的图表如下所示：

enter image description here

情节清楚地表明一个信号滞后于另一个。因此，我想计算信号之间的平均相移。为此，我尝试了以下方法：

Nfft = 512;
n = 50;
Fs = 6;
[Pxy,~] = cpsd(vv(:,2),vv(:,3),hamming(n),n/2,Nfft,Fs);
coP = real(Pxy);
quadP = imag(Pxy);
phase = atan2(coP,quadP);
Sphase = nanmean(phase);
Sphase = Sphase * 180 / pi;

给出了

Sphase = 18.40

我所演示的方法是否有意义，是否正确？

Answer 1

如评论中所述，一个选项是使用低通滤波器预处理信号。这可以在傅里叶域中方便地完成。我使用了互相关函数的乘法与an image registration application中不同的截止值。

适应您的问题，它看起来像是（从this excellent answer复制的部分代码）：

N = size(vv, 1);
nfft = 2^nextpow2(2*N-1);
F=fft(vv(:,2), nfft);
M=fft(vv(:,3), nfft);

R=F.*conj(M);

扫描截断滤波和逆FFT：

r = ones(nfft,1);

for k = 0.1:0.05:0.9
    r = ifft(R(1:end-ceil(k*nfft)));
    r = r.*r;
end

估算翻译：

rmax = max(abs(r));
x = find(abs(r) == rmax);

现在，让我们看一下相关函数：

corrfun

很明显，最大值不是相关峰值的中心。 在高峰附近拟合高斯会更合适。这是子像素注册的典型方法。

让我们尝试10％的邻居：

f = fit((1:2*ceil(0.05*N)).', abs(r(x-ceil(0.05*N):x+ceil(0.05*N)-1)),'gauss1');

高斯的中心被发现为 24.94 样本，这与您的估计有些一致。你的方法似乎在某种程度上起作用，我的猜测是差异是由于信号的平滑。

修正后的曲线：

results

两个噪声信号之间的平均相移

1 个答案: