适用于1D的opencv dft vs.matlab fft [英] opencv dft vs. matlab fft for 1D
本文介绍了适用于1D的opencv dft vs.matlab fft的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！
问题描述
这是我输入的一维数组:
[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]
我跑步时
Matlab fft我得到的结果不同于
Matlab的答案:
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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，某些值是相同的:
[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一种方法可以得到与matlab相同的结果? 此数字 -4.3160208e + 008，-4.3160208e + 008 反复出现.这是转换问题吗?
解决方案
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，或者说波数.
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，它将光谱的负数部分置于正数附近.
现在，由于上述实数据傅里叶变换的对称性，多余的表示傅里叶频谱的两个半部(一个只是另一个的复共轭)是多余的. Matlab还是这么做的，但是对于OpenCV似乎不是这样.如果您注意到的话，OpenCV输出的后半部分会出现一个奇怪的数字-4.3160208e + 008，在我看来，这只是某种虚拟填充. 基本上，您应该忽略输出的后半部分，实际输出仅是前半部分.this is my input 1D array:
[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]
when I run
Matlab fft I get different results than
answer from Matlab:
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 - 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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 output please note that some of the values are the same:
[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, 1.9662709, 1.8409662, -0.9237324, 0.3887701, 0.83835888, 1.1778173, 0.40068072, 0.2591362, -1.805531, 0.37266827, 0.085778832, -0.46706057, 0.019422591, -0.78862524, -0.72800255, -0.52543736, 1.0548751, 1.0942721, 2.3556924, 1.2972126, -0.92645401, 0.65454626, -0.24292475, 1.4631515, 0.51448888, 1.5789657, -0.94608289, 0.99792957, -3.9589138, -2.1106853, -1.8556111, -2.8534913, -0.66516978, -3.6764612, 1.493674, 2.0280688, 3.4307818, 0.58782125, -0.66583544, -0.88579464, -0.27679062, -0.28537679, -0.37455428, -1.7532051, 2.1291695, -0.39484131, 1.598603, 0.77090323, 1.8497298, 1.8382895, 2.3185685, 1.0264703, 0.99646896, 3.0183427, 0.52932495, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, 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-4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, -4.3160208e+008, 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Can you please tell me if there is a way to get the same result as matlab? this number -4.3160208e+008, -4.3160208e+008 appears over and over. is this a conversion problems?
解决方案
You are taking the fft of real data, therefore the Fourier coffees have the Hermite symmetry c(k)=conjugate(c(-k)), where k is the index of the coefficient, or the wavenumber if want to say so.
Matlab arranges the output like this
[c(0),c(1),c(2),...,c(N/2),c(-N/2),c(-N/2+1),...,c(-1)]
in other words it puts the negative part of the spectrum next to the positive one.
Now, due to the aforementioned symmetry of real-data Fourier transform, it is redundant to represent both halfs of the Fourier spectrum (one is just the complex conjugate of the other). Matlab does it anyway, but it doesn't seem to be the case for OpenCV. If you note, the weird number -4.3160208e+008 appears on the second half of the OpenCV output, and it seems to me that this is just some sort of dummy padding. Basically, you should just disregard this second half of the output, the real output is just the first half.
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