C++ opencv dft与matlab fft的1D比较

这是我的输入1D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]

当我跑的时候 Matlab

fft

我得到的结果与

Matlab的答案是：

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);

你能告诉我是否有办法得到与matlab相同的结果吗？

---

该数字-4.3160208e+008，-4.3160208e+008反复出现。这是一个转换问题吗？

您正在对实际数据进行

fft

，因此傅里叶咖啡具有厄米对称性

c（k）=共轭（c（-k））

，其中

k

是系数的指数，或者如果愿意的话，是波数

Matlab这样安排输出

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

换句话说，它把光谱的负部分放在正部分的旁边

现在，由于上述真实数据傅里叶变换的对称性，表示傅里叶光谱的两个半部分是多余的（一个是另一个的复共轭）。不管怎么说，Matlab是这样做的，但OpenCV似乎不是这样。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

为了将来的参考，此测试在1D内与matlab的结果有点精确

    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);
    }   

cv:：Mat ff；
cv:：dft（距离F、ff、cv:：dft_行| cv:：dft_复数_输出）；
//为复杂的和真实的价值创造位置
cv:：Mat平面[]={cv:：Mat:：zeros（distanceF.size（），1，CV32f），cv:：Mat:：zeros（distanceF.size（），1，CV32f）}；
cv:：拆分（ff，平面）；//平面[0]=Re（DFT（I），平面[1]=Im（DFT（I））
int m=平面[0].cols；
内部枢轴=天花板（m/2）；
//使用复共轭复制FFT结果，以获得精确的matlab结果
对于（int i=pivot+1，k=pivot；i

您能显示不同的结果吗？@Kornel我添加了标志DFT\u行，还添加了results@caludv你的意思是，matlab返回227个复数，我需要忽略其中的一半？open cv返回454个数，这是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输出良好，具有冗余，因为它包含两个半频谱。这取决于您在下面的计算中是否需要同时使用这两个或仅使用前半部分（以提高效率）。在开放式简历中，你必须把下半部分（全部是-4.3160208e+008）剔除掉，因为这只是垃圾。是的，openCV将结果存储在一个2*N的实数组中（real，imag，real，imag，…），而Matlab使用一个N的复数数组。@caludv我怎样才能从openCV DFT中看到输出矩阵的一个值？我如何从ff矩阵中得到它，它是一个cv:：mat，我不知道它在DFT后的类型，例如，位置0处的值？我通常使用ff.at（0）之类的东西；但它在比赛结束后就不起作用了DFT@Caludev那么openCV只恢复了频谱的一半？我能让它两半都退吗？

    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);
    }