一维的opencv dft与matlab fft

Posted 2023-02-22

【中文标题】一维的opencv dft与matlab fft

【英文标题】：opencv dft vs. matlab fft for 1D

【发布时间】：2015-03-24 12:27:42

【问题描述】：

这是我的输入一维数组：

 [13.9284, 14.5602, 15.5242, 16.4924, 17.4642, 18.2483, 19.2354, 20.2237, 21.095, 21.0238, 22, 23, 24.0208, 23.0868, 24.1868, 25.1794, 26.0768, 27.074, 28.0713, 27.074, 26.0768, 25.0799, 24.0208, 25, 26, 27, 28, 27.0185, 28.0713, 29.0689, 30.0167, 30, 30, 30.0167, 31, 32, 33.0151, 34.0147, 33, 32, 31.0161, 32.0624, 33.1361, 34.0588, 35.0571, 36.0139, 36, 37, 38.0132, 37.054, 37.1214, 36.2215, 35.2278, 34.1321, 33.2415, 33.3766, 34.5254, 35.5106, 36.6742, 37.6563, 36.6742, 35.5106, 34.5254, 33.3766, 32.3883, 31.257, 30.1496, 29.2746, 29.4279, 30.5941, 30.8058, 30.0832, 29.1204, 28.1603, 27.2029, 25.9615, 25.2982, 24.0416, 23.0868, 22.1359, 21.1896, 20.2485, 19.3132, 18.3848, 17.088, 16.1555, 15.2315, 14.3178, 13.4164, 12.53, 11.1803, 10.2956, 9.43398, 8.60233, 7.81025, 6.40312, 5.65685, 5, 4.47214, 4.12311, 4, 3, 3.16228, 3.60555, 4.24264, 5, 5.83095, 6.7082, 7.28011, 8.24621, 9.21954, 10.198, 11.0454, 12.0416, 13.0384, 14.0357, 15.0333, 16.0312, 17.0294, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28.0179, 29.0172, 30.0167, 31.0161, 32.0156, 33.0151, 34.0147, 35.0143, 36.0555, 37.054, 38.0526, 39.0512, 40.05, 41.1096, 42.107, 43.1045, 44.1022, 45.0999, 46.0977, 47.0956, 48.1664, 49.163, 50.1597, 51.1566, 52.2398, 53.2353, 54.231, 55.2268, 56.2228, 55.2268, 54.231, 53.2353, 52.2398, 51.2445, 50.2494, 49.2544, 48.2597, 47.2652, 46.2709, 45.2769, 44.2832, 43.2897, 42.2966, 41.3038, 40.3113, 39.3192, 38.3275, 37.3363, 36.3456, 35.3553, 34.3657, 33.3766, 32.3883, 31.4006, 30.4138, 29.4279, 28.4429, 27.4591, 26.4764, 25.4951, 24.5153, 23.5372, 22.561, 21.587, 20.6155, 19.6469, 18.6815, 17.72, 16.7631, 15.8114, 14.8661, 13.9284, 13, 12.083, 11.1803, 10.2956, 9.43398, 8.60233, 7.81025, 7.07107, 6.40312, 5.83095, 5.38516, 5.09902, 5, 5, 5.09902, 5.38516, 5.83095, 6.40312, 7.07107, 7.81025, 8.60233, 9.43398, 10.2956, 11.1803, 12.083, 13]

当我跑步时 Matlab fft 我得到的结果不同于

来自 Matlab 的回答：

5850.44082000000 + 0.00000000000000i    -236.195108992328 + 494.327104308963i   -1601.71373056680 - 1257.19679210623i   401.270621054570 - 54.8348065835625i    58.6362849360901 - 163.991208417496i    -81.1618489916308 - 60.6727729546051i   98.2137509701359 - 178.874979649065i    8.75660326872264 + 31.1059211928010i    -14.4396596622584 - 7.65407579243336i   -9.18663229218099 - 27.1997908482849i   32.5503165463479 + 24.3192745247901i    -31.1219011708661 + 25.7860663846281i   2.95031666949167 + 6.15041271891396i    15.5915878000708 + 7.44141735494909i    6.97702383662843 + 35.5170021796418i    23.6281937003968 - 21.1006242353996i    5.97648257401926 - 39.6138615794895i    -33.0032997489133 + 1.30076978156147i   -15.0418122371750 + 24.6819515735041i   31.1393323965219 - 10.0379855452569i    -8.54814236721161 - 24.2416895900915i   -39.1574989954314 + 6.70015288183043i   -5.60660423183304 + 23.6679501739800i   19.1780240882932 + 15.5704394051741i    1.30717784406095 + 3.68504588500404i    7.45795750406563 + 3.39486331858465i    17.5245792950556 - 4.31294325456059i    2.41873595069340 - 7.44453173664043i    -6.00947311352358 - 12.1313710088946i   -4.18154377130777 - 2.50225243762004i   -2.20651365633251 + 4.72665264429753i   -1.72270341112623 + 0.197689181530038i  3.48935944436198 - 8.66327988659334i    -11.8221389770113 - 2.73492738484021i   -13.4251149477799 + 12.7213800072862i   3.73623581925574 + 12.7809120584468i    13.9007662712349 + 8.74121680636068i    6.24770455302712 - 2.00106833739501i    6.18955793386744 - 1.78052956088457i    9.37882547144118 - 10.4387804557484i    -10.2820486114914 - 7.56460553957821i   -6.91793379409868 + 3.37859410905941i   2.26246595365120 + 2.85055700831106i    2.97164192031584 + 1.19638197424677i    -2.32764734219557 - 3.52146253780298i   -0.128456276053257 + 0.371511723725504i 2.51404210613061 - 0.368321502067278i   -3.36759807322456 - 1.99977119992005i   -0.550861771421822 - 0.781259371882626i 0.654734330528342 - 1.10909753428241i   -5.10226403227105 - 0.649609303524812i  -4.35743957552811 + 2.03780871572405i   0.789562920892216 + 5.02843929868241i   1.31772372300086 + 3.20064305370176i    -0.140064442432518 + 0.715606830659397i 2.55731297616605 + 1.22415928937412i    0.972383057822540 + 1.11452954184361i   -1.09766497930718 + 0.128751181670111i  0.295033690905171 + 0.753971522354846i  1.55444641432210 + 3.35145255172278i    0.374562941292385 + 2.08937979612806i   5.29852099293259 + 1.37829167261507i    5.54859012001244 - 3.21257680351025i    -1.07668822076172 - 3.30955388709968i   -1.37257720079793 - 2.44245043665786i   1.40536606890888 + 1.66440564981678i    2.49435403989193 - 2.58415130217770i    -3.28563738557140 - 4.05477826915994i   -0.518407813348183 + 0.131067263982409i -2.04925759851836 - 0.262283316140675i  -2.41969646059706 + 0.777798355648820i  -0.134139765532215 + 0.907106120270047i 0.730399953450643 + 1.65851073839491i   -1.45678885233597 - 1.16372102129882i   -2.20160324624550 + 1.32325219820590i   0.579604238352069 + 3.38240693896227i   0.831075445733614 + 3.24321494006862i   4.28901429023598 - 0.0874581930640304i  1.49823315525401 - 2.39040184090840i    -0.377513297736293 + 1.16391842543968i  2.06813869338537 - 1.19345092081081i    2.05985213152420 - 2.22716482633267i    -0.442563051798736 - 3.60274864824367i  -5.60740416812049 - 2.10873191433014i   -2.28409332116379 + 3.25751007842877i   0.433042603344951 + 3.05868696142239i   1.02072812804223 + 1.96653338929739i    1.84085146695848 - 0.923985120389667i   0.388629240309292 + 0.838212051807965i  1.17786879322356 + 0.400582810627874i   0.259566861526970 - 1.80532655327674i   0.372659878189257 + 0.0860665525151383i -0.467279393929562 + 0.0194961351504794i    -0.788639270316992 - 0.728110745822363i -0.525425582048058 + 1.05458284528174i  1.09457353336624 + 2.35618849514349i    1.29718434477957 - 0.926336813481122i   0.654663687830375 - 0.243309093614304i  1.46292093798042 + 0.514645032758256i   1.57935027555005 - 0.946259927194781i   0.997945072809900 - 3.95889770752841i   -2.11126597496163 - 1.85525696046438i   -2.85375151259268 - 0.665127010849972i  -3.67649131275672 + 1.49357708053631i   2.02842018202423 + 3.43084304311646i    0.587989734036455 - 0.665601892824327i  -0.885597237730284 - 0.276649300905060i -0.285389790393298 - 0.374323003019116i -1.75323182180390 + 2.12902138070610i   -0.394442022274234 + 1.59875943868965i  0.770938958112609 + 1.84913363734508i   1.83828912016749 + 2.31866799695042i    1.02615442076382 + 0.996282806003860i   3.01830600098366 + 0.528644305273687i   3.01830600098366 - 0.528644305273687i   1.02615442076382 - 0.996282806003860i   1.83828912016749 - 2.31866799695042i    0.770938958112609 - 1.84913363734508i   -0.394442022274234 - 1.59875943868965i  -1.75323182180390 - 2.12902138070610i   -0.285389790393298 + 0.374323003019116i -0.885597237730284 + 0.276649300905060i 0.587989734036455 + 0.665601892824327i  2.02842018202423 - 3.43084304311646i    -3.67649131275672 - 1.49357708053631i   -2.85375151259268 + 0.665127010849972i  -2.11126597496163 + 1.85525696046438i   0.997945072809900 + 3.95889770752841i   1.57935027555005 + 0.946259927194781i   1.46292093798042 - 0.514645032758256i   0.654663687830375 + 0.243309093614304i  1.29718434477957 + 0.926336813481122i   1.09457353336624 - 2.35618849514349i    -0.525425582048058 - 1.05458284528174i  -0.788639270316992 + 0.728110745822363i -0.467279393929562 - 0.0194961351504794i    0.372659878189257 - 0.0860665525151383i 0.259566861526970 + 1.80532655327674i   1.17786879322356 - 0.400582810627874i   0.388629240309292 - 0.838212051807965i  1.84085146695848 + 0.923985120389667i   1.02072812804223 - 1.96653338929739i    0.433042603344951 - 3.05868696142239i   -2.28409332116379 - 3.25751007842877i   -5.60740416812049 + 2.10873191433014i   -0.442563051798736 + 3.60274864824367i  2.05985213152420 + 2.22716482633267i    2.06813869338537 + 1.19345092081081i    -0.377513297736293 - 1.16391842543968i  1.49823315525401 + 2.39040184090840i    4.28901429023598 + 0.0874581930640304i  0.831075445733614 - 3.24321494006862i   0.579604238352069 - 3.38240693896227i   -2.20160324624550 - 1.32325219820590i   -1.45678885233597 + 1.16372102129882i   0.730399953450643 - 1.65851073839491i   -0.134139765532215 - 0.907106120270047i -2.41969646059706 - 0.777798355648820i  -2.04925759851836 + 0.262283316140675i  -0.518407813348183 - 0.131067263982409i -3.28563738557140 + 4.05477826915994i   2.49435403989193 + 2.58415130217770i    1.40536606890888 - 1.66440564981678i    -1.37257720079793 + 2.44245043665786i   -1.07668822076172 + 3.30955388709968i   5.54859012001244 + 3.21257680351025i    5.29852099293259 - 1.37829167261507i    0.374562941292385 - 2.08937979612806i   1.55444641432210 - 3.35145255172278i    0.295033690905171 - 0.753971522354846i  -1.09766497930718 - 0.128751181670111i  0.972383057822540 - 1.11452954184361i   2.55731297616605 - 1.22415928937412i    -0.140064442432518 - 0.715606830659397i 1.31772372300086 - 3.20064305370176i    0.789562920892216 - 5.02843929868241i   -4.35743957552811 - 2.03780871572405i   -5.10226403227105 + 0.649609303524812i  0.654734330528342 + 1.10909753428241i   -0.550861771421822 + 0.781259371882626i -3.36759807322456 + 1.99977119992005i   2.51404210613061 + 0.368321502067278i   -0.128456276053257 - 0.371511723725504i -2.32764734219557 + 3.52146253780298i   2.97164192031584 - 1.19638197424677i    2.26246595365120 - 2.85055700831106i    -6.91793379409868 - 3.37859410905941i   -10.2820486114914 + 7.56460553957821i   9.37882547144118 + 10.4387804557484i    6.18955793386744 + 1.78052956088457i    6.24770455302712 + 2.00106833739501i    13.9007662712349 - 8.74121680636068i    3.73623581925574 - 12.7809120584468i    -13.4251149477799 - 12.7213800072862i   -11.8221389770113 + 2.73492738484021i   3.48935944436198 + 8.66327988659334i    -1.72270341112623 - 0.197689181530038i  -2.20651365633251 - 4.72665264429753i   -4.18154377130777 + 2.50225243762004i   -6.00947311352358 + 12.1313710088946i   2.41873595069340 + 7.44453173664043i    17.5245792950556 + 4.31294325456059i    7.45795750406563 - 3.39486331858465i    1.30717784406095 - 3.68504588500404i    19.1780240882932 - 15.5704394051741i    -5.60660423183304 - 23.6679501739800i   -39.1574989954314 - 6.70015288183043i   -8.54814236721161 + 24.2416895900915i   31.1393323965219 + 10.0379855452569i    -15.0418122371750 - 24.6819515735041i   -33.0032997489133 - 1.30076978156147i   5.97648257401926 + 39.6138615794895i    23.6281937003968 + 21.1006242353996i    6.97702383662843 - 35.5170021796418i    15.5915878000708 - 7.44141735494909i    2.95031666949167 - 6.15041271891396i    -31.1219011708661 - 25.7860663846281i   32.5503165463479 - 24.3192745247901i    -9.18663229218099 + 27.1997908482849i   -14.4396596622584 + 7.65407579243336i   8.75660326872264 - 31.1059211928010i    98.2137509701359 + 178.874979649065i    -81.1618489916308 + 60.6727729546051i   58.6362849360901 + 163.991208417496i    401.270621054570 + 54.8348065835625i    -1601.71373056680 + 1257.19679210623i   -236.195108992328 - 494.327104308963i

openCV 2.4.10：

cv::vector<float> distanceF; // this is the type of the vector
cv::dft(distanceF, ff, cv::DFT_ROWS|cv::DFT_COMPLEX_OUTPUT);

OpenCV 输出请注意有些值是一样的：

[5850.4424, 0, -236.19542, 494.32721, -1601.7139, -1257.1968, 401.27112, -54.834793, 58.635941, -163.99118, -81.161819, -60.672802, 98.213882, -178.8752, 8.7567081, 31.105858, -14.439482, -7.6539149, -9.1864853, -27.199965, 32.550457, 24.319056, -31.122013, 25.786121, 2.9505329, 6.1505966, 15.59177, 7.4411783, 6.9766369, 35.51675, 23.628296, -21.100199, 5.9758949, -39.613434, -33.00349, 1.3006741, -15.041353, 24.681818, 31.139578, -10.038104, -8.5481758, -24.24147, -39.157513, 6.7004414, -5.6067162, 23.668552, 19.177927, 15.570613, 1.3069649, 3.6849215, 7.4576416, 3.3949444, 17.524834, -4.3131351, 2.4190979, -7.4447069, -6.009819, -12.131269, -4.1815758, -2.5021544, -2.2066612, 4.7267613, -1.722599, 0.1980657, 3.4889717, -8.66294, -11.822751, -2.7352583, -13.425085, 12.721531, 3.7364502, 12.780836, 13.900464, 8.7409039, 6.2476082, -2.000788, 6.1896486, -1.7802718, 9.3790874, -10.438701, -10.282202, -7.5648155, -6.9182959, 3.3786888, 2.2623367, 2.8504691, 2.9716797, 1.1957676, -2.3280506, -3.521215, -0.12844467, 0.37162167, 2.513998, -0.36863309, -3.3680859, -1.9997617, -0.55117607, -0.78108609, 0.6547966, -1.1083429, -5.1021919, -0.64962733, -4.3571014, 2.0373371, 0.78962708, 5.0286837, 1.3172665, 3.2008133, -0.14001274, 0.71585965, 2.5574074, 1.2240793, 0.97222137, 1.1142333, -1.0971603, 0.12921375, 0.29561615, 0.75393069, 1.5542717, 3.3511853, 0.37465286, 2.0893302, 5.2984409, 1.3784981, 5.548686, -3.2126107, -1.076519, -3.3098588, -1.3726921, -2.4427652, 1.4058294, 1.6643414, 2.4948006, -2.5840356, -3.2862215, -4.0548897, -0.51816654, 0.13079435, -2.0494299, -0.26226592, -2.4197426, 0.77750373, -0.13409233, 0.90709144, 0.73083496, 1.6584089, -1.4566784, -1.163747, -2.2017193, 1.3230393, 0.57952499, 3.3821714, 0.83114338, 3.2429562, 4.2885866, -0.087527037, 1.4980612, -2.3904862, -0.37744904, 1.1637971, 2.0684986, -1.1937973, 2.0592871, -2.227041, -0.44268799, -3.6024194, -5.6071653, -2.1089995, -2.2843628, 3.2571955, 0.43229103, 3.0588517, 1.0210943, 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能否请您告诉我是否有办法获得与 matlab 相同的结果？ 这个数字 -4.3160208e+008, -4.3160208e+008 一遍又一遍地出现。这是转换问题吗？

【问题讨论】：

你能展示不同的结果吗？

@Kornel 我添加了标志 DFT_ROWS 并添加了结果

【参考方案1】：

以供将来参考，此测试与 matlab 的 1D 结果有点准确

    cv::Mat ff;
    cv::dft(distanceF, ff, cv::DFT_ROWS|cv::DFT_COMPLEX_OUTPUT);

    //Make place for both the complex and the real values
    cv::Mat planes[] = cv::Mat::zeros(distanceF.size(),1, CV_32F), cv::Mat::zeros(distanceF.size(),1, CV_32F);
    cv::split(ff, planes);                   // planes[0] = Re(DFT(I), planes[1] = Im(DFT(I))

    int m = planes[0].cols;
    int pivot = ceil(m/2);
    //duplicate FFT results with Complex conjugate in order to get exact matlab results

    for (int i = pivot + 1, k = pivot; i < planes[1].cols; i++, k--)
    
         planes[1].at<float>(i) = planes[1].at<float>(k) * -1; 
         planes[0].at<float>(i) = planes[0].at<float>(k);
       

【参考方案2】：

您正在获取真实数据的fft，因此傅立叶咖啡具有 Hermite 对称性c(k)=conjugate(c(-k))，其中k 是系数的索引，或者如果想说的话是波数。

Matlab 是这样排列输出的

[c(0),c(1),c(2),...,c(N/2),c(-N/2),c(-N/2+1),...,c(-1)]

换句话说，它将频谱的负部分放在正部分旁边。

现在，由于上述真实数据傅里叶变换的对称性，表示傅里叶谱的两半是多余的（一个只是另一个的复共轭）。 Matlab 无论如何都会这样做，但 OpenCV 似乎并非如此。如果您注意到，奇怪的数字 -4.3160208e+008 出现在 OpenCV 输出的后半部分，在我看来这只是某种虚拟填充。 基本上，你应该忽略输出的后半部分，真正的输出只是前半部分。

【讨论】：

@caludv 所以你是说，matlab 返回 227 个复数，我需要忽略其中的一半？并且 open cv 返回 454 个数字，它们是 227 个复数（1 表示实数，1 表示虚数），我也应该忽略其中的一半）？

Matlab 输出都很好，有冗余，因为它包含频谱的两半。由您决定在以下计算中是否需要同时使用前半部分或仅使用前半部分（以提高效率）。使用打开的简历，您必须删除下半部分（所有-4.3160208e + 008），因为它只是垃圾。是的，open cv 将结果存储在 2*N 实数数组（real,imag,real,imag,...）中，而 Matlab 使用 N 复数数组。

@caludv 如何从 openCV DFT 中查看输出矩阵的一个值？

我如何从 ff 矩阵中获取 cv::mat ，我不知道它是 DFT 后的类型，例如位置 0 处的值？我通常使用类似 ff.at(0);但它在 DFT 之后不起作用

@Caludev 所以openCV只恢复了一半的频谱？我可以让它返回两半吗？