根据ECG流计算心率-java/Nymi波段

我试图使用Nymi波段提供的ECG数据流来计算用户的心率。我目前的方法是通过Nymi Bands ECG流获取10秒的ECG数据样本，检查心跳并乘以6得到BPM。通过从当前值中减去之前的值并将其存储在一个列表中，我得到了一个相当精确的ECG流图。问题是，我很难准确地确定心跳实际发生的时间

我的猜测是，我需要首先应用某种形式的过滤器，以确保“噪音”不会对读数产生负面影响。所以我的问题是：有没有更干净、更准确的方法来分析可能的心跳数据？或者我怎样才能正确地过滤数据以消除“噪音”

---

编辑1（代码和样本数据）：

-第一种方法：我使用Chauvenet标准的一种变体来尝试捕捉异常值，这将代表心跳。然而，标准偏差总是太高，平均值太低（几乎总是负值），无法准确检测哪些值是异常值。 使用样本数据（如下），结果为10秒内22次：

private List<Integer> parseDataForHB(List<Integer> ecgValues)
{
    double mean = mean(ecgValues);
    double standardDeviation = standardDeviation(ecgValues);
    Iterator it = ecgValues.iterator();

    List<Integer> heartBeatValues = new ArrayList<>();

    NormalDistribution normalDistribution = new NormalDistribution(mean, standardDeviation);
    while(it.hasNext())
    {
        int ecgVal = (Integer) it.next();
        stringBuilder.append(", " + ecgVal);

        if((normalDistribution.cumulativeProbability((double)ecgVal) * ecgValues.size()) < 0.5)
        {
            heartBeatValues.add(ecgVal);
        }
    }
    return heartBeatValues;
}

private List<Integer> parseDataForHB(List<Integer> ecgValues, int averageHeartBeatValue)
{
    int previousVal = 0;
    List<Integer> heartBeatValues = new ArrayList<>();
    Iterator it = ecgValues.iterator();

    while(it.hasNext())
    {
        int ecgVal = (Integer)it.next();
        if(ecgVal >= (averageHeartBeatValue * .5))
        {
            if(((ecgVal > 0) && (previousVal < 0)) ||
                    ((ecgVal < 0) && (previousVal > 0)))
            {
                heartBeatValues.add(ecgVal);
                averageHeartBeatValue = (int) mean(heartBeatValues);
            }
        }
        previousVal = ecgVal;
    }
    return  heartBeatValues;
}

---

这个数据样本有更多的“噪音”，理想情况下我想过滤掉：

-35751, -32565, -28033, -23493, -18135, -10310, -8731, -4143, -5485, -2162, -955, -6393, -4211, -3047, -3097, -3232, -2975, -1571, -2105, -1440, -3880, -372, -227, -1266, -2269, -299, 2255, -2534, -3677, 675, 78, 415, -2274, -2256, 875, -13756, -5896, 15991, 585, -4356, 2706, -2028, 2127, -2249, -1282, -2555, -2865, -2570, -2666, 3745, 5965, 2728, -73, 611, 342, 1297, 214, -1153, 496, -283, -1868, 1791, -541, 2044, -414, 1595, 72, -2262, -363, 1855, -649, 909, -815, -363, 2791, 152, 1072, -2025, 1291, -12311, -6729, 22739, -4036, -784, 2598, -871, -2182, 1244, -2158, -2403, -1551, -3825, -4385, 4281, 5919, 6609, -2120, 480, 1070, -736, 525, -1520, -2225, 1795, 574, 781, -584, -1750, 175, 3339, -1175, 1186, -1319, 361, 885, -46, -1078, -2569, -720, 1533, 2465, 113, -1953, 2475, -5732, -22272, 24177, 235, 1385, -3850, 2291, -1417, -2452, -862, -3745, -932, -3586, -3987, -69, 5431, 3902, 2284, -619, 609, -1424, -1467, -1055, -1166, -1216, 1515, -1851,  -49, -4983, 1495, 3563, -873, -1933, -397, -933, 546, -1925, -753, -53, -2603, -591, 769, 3005, -2773, 2097, -5993, -21911, 23700, 3747, -4986, 595, -1815, -1589, -571, -2116, -1823, -6708, -1686, -1891, -991, 5178, 3719, 1188, -2394, 3992, -1555, -5306, 2830, 25, -2564, 2112, -1723, -3810, 4700, -2780, 520, -70, -2015, 1093, -2231, 2526,  -4651, -799, 764, -2429, 272, -564, 1119, -1089, 2371, -5627, -8118, 7574, 6499, -8635, 582, -2186, -1986, -477, -2178, -707, -6743, -3582,  -4409, 1806, 2718, 5820, -272, 1046, -580, -1552, -1184, -3206, -690, 1218, -871, -1919, -2552, 2127, -754, -1848, -3573, 3112, -1170, 468, -2593, -382, -3280, 3664, -5572, 1992, -30, -7230, 8670, -2504, -4969, -14813, 225, 14109, 8194, -9438, -4781, 3102, -8626, 6428, -5387, -5050, 548, -10060, 6965, -2155, 2195, 5498, 359, -4090, 5130, -4214, 1478, -364, -6444, 5889, -3363, -1621, -3570, 8390, -5828, -1472, 841, -8869, 11057, -6734, 173, 535, -638, -2628, -2751, 4754, 514, -2423, 1168, -3860, -23875, 18070, 7511, -3048, -1173, -6033, 5087, -5258, -3012, -831, -1180, -5298, -557, -2993, 6236, 1417, 2683, 361, 2293, -4117, 1122, -1922, -3730, 2705, -848, -3560, 2100, -319, -495, -347, -2329, 1341, -805, 1227, -2463, -440, -1440, 1206, -2361, -411, -1481, 3837, -3101, 1851, -5779, -22183, 22335, 3443, -3854, -2077, -2311, 1471, -817, 792, -7227, -2963, -4038, -92, -1234, 4692, 3973, 2122, 1333, -222, -2997, 1279, -3531, 1335, 140, -375, -2235, 2795, 598, -3233, -951, 1895, -288, -925, 1066, -3400, -1230, -2011, 2217, 1942, -1790, -1700, -1450, 756, -10710, -6744, 18590, -1435, -1739, -2097, -2638, -454, 67, -4556, -695, -5602, -2815, -2142, 764, 5958, 2175, 2055, -647, -466, -478, -1082, 527, -2214, 275, 274, -1687, -2358, 31, 1570, -1587, -871, -271, -2365, 1337, -831, -1095, -2056, -208, -1383, 2415, -1523, -1538, -719, -3842, -20933, 15223, 9978, -4030, -2521, 190, -4163, -2305, 1814, -2465, -4207, -3792, -2559, -2123, 2908, 5366, 2933, -1455, -57, 112, -2241, -1416, -2778, 2353, -1200, -2027, -962, 1117, -1530, 157, -2902, 3466, -5072, 555, 1425, -2791, -1369, 156, -6789, 1961, -1111, 3631, -2592, -1643, 2039, -2865

---

更新1-根据@stackoverflowuser2010建议，我尝试使用FFS将ECG数据转换为频谱，以计算实际频率的峰值。然而，当通过方法1（Chauvenet标准）或方法2（基于平均心跳值的计算）时，这里的结果并没有更好。也许我遗漏了什么？以下是使用相同数据集的结果：

TransformType.FORWARD:进近1=1，进近2=266

TransformType.INVERSE：方法1=1，方法2=0

我认为部分问题是为了使用FFT，数据必须是2的幂。由于数据流的大小不同（记录10秒，更快的心跳将生成更大的数据集），如果数据集的大小不是2的幂，我必须填充数据集的末尾

以下是FFT功能的新代码：

 private List<Integer> ffs(List<Integer> ecgValues)
{
    List<Integer> transoformedStream = new ArrayList<>();
    FastFourierTransformer ffs = new FastFourierTransformer(DftNormalization.STANDARD);
    double[] input = convertToDoubleArray(ecgValues);

    Complex[] complex = ffs.transform(input, TransformType.FORWARD);

    for(int i = 0; i < complex.length - 1; i++)
    {
        double real = (complex[i].getReal());
        double imaginary = (complex[i].getImaginary());

        transoformedStream.add((int)Math.sqrt((real * real) + (imaginary * imaginary)));
    }

    return transoformedStream;
}

private double[] convertToDoubleArray(List<Integer> ecgValues)
{
    double[] convertedList;

    if(isPowerOfTwo(ecgValues.size()))
    {
        convertedList = new double[ecgValues.size()];
    }
    else
    {
        convertedList = new double[nextPowerOfTwo(ecgValues.size())];
    }

    for(int i = 0; i < ecgValues.size(); i++)
    {
        convertedList[i] = (double)ecgValues.get(i);
    }
    return convertedList;
}

private boolean isPowerOfTwo(int size)
{
    boolean isPowerOfTwo = ((size & -size) == size);

    return isPowerOfTwo;
}

private int nextPowerOfTwo(int size)
{
    int res = 2;
    while (res <= size) {
        res  *= 2;
    }

    return res;
}

---

更新2-继续处理FFT数据，但仍不确定我在这里的路径是否正确。使用上面列出的用于FFT的相同方法（使用“org.apache.commons.math3.transform.FastFourierTransformer”），我搜索FFT结果中的峰值。由于这个值太高，我采用了我发现的另一种方法，这里用峰值乘以信号频率（在本例中为50），然后除以样本量。对于下面的示例，其计算如下：

50hz*423079（峰值）/510（样本量）=41478.33

或者：

50hz*179（峰值指数）/510（样本量）=17.54

以下是ECG值：

-70756.0, -56465.0, -52389.0, -25199.0, -20352.0, -13660.0, -12615.0, -9202.0, -10225.0, -6168.0, -5338.0, 4409.0, -1204.0, 3009.0, 1821.0, -3127.0, 2076.0, 720.0, 675.0, -880.0, 622.0, 1851.0, -915.0, 1296.0, -3069.0, -10.0, 1114.0, 2335.0, -4363.0, 3386.0, -189.0, -2497.0, 6326.0, -4007.0, -2708.0, 1120.0, -2159.0, 2643.0, -1817.0, 749.0, 6096.0, -2927.0, -1514.0, -24006.0, 18897.0, 10851.0, -2934.0, -1487.0, -1660.0, 90.0, 1999.0, -4448.0, 2567.0, -1185.0, -2172.0, -4479.0, -253.0, 5173.0, 5956.0, 2814.0, 3279.0, 1617.0, 5174.0, -4152.0, 911.0, 2404.0, 1579.0, 792.0, 573.0, -28.0, 3251.0, 159.0, -2170.0, 727.0, 2652.0, -2676.0, 3039.0, -2938.0, 2539.0, 1586.0, -1447.0, 132.0, -60.0, 439.0, -87.0, -2239.0, 2074.0, 1268.0, -3559.0, 1266.0, -18937.0, -869.0, 25032.0, -6298.0, -1653.0, 590.0, -1737.0, -3840.0, -484.0, -3408.0, -2470.0, -3663.0, -1526.0, -158.0, -748.0, 5249.0, -44.0, 1903.0, -1900.0, 2513.0, -58.0, -2065.0, -450.0, -1131.0, -2262.0, 3663.0, -2968.0, 1262.0, -1687.0, -2745.0, -581.0, -11.0, -528.0, 349.0, -2231.0, -1198.0, -2039.0, 1362.0, -3671.0, 580.0, -794.0, -3924.0, -1711.0, 2093.0, -935.0, 2423.0, -1017.0, -5674.0, -26830.0, 27284.0, 4433.0, -4604.0, -2655.0, -4541.0, -2643.0, 2036.0, -3159.0, -3194.0, -2030.0, -2535.0, -5753.0, -31.0, 5056.0, 241.0, 4452.0, -1591.0, -1056.0, 573.0, -3637.0, -1224.0, -2728.0, 3535.0, -2645.0, -1281.0, -1359.0, -1918.0, 621.0, -2967.0, 2535.0, -3048.0, -2820.0, -2530.0, -1202.0, 315.0, -645.0, -3541.0, -3547.0, -2725.0, -4590.0, -124.0, 620.0, -1866.0, -4450.0, -17536.0, 4480.0, 16119.0, -7421.0, 2363.0, -8373.0, 3109.0, -896.0, -6533.0, -1502.0, -378.0, -3602.0, -5893.0, -2730.0, 2619.0, 3532.0, 675.0, -778.0, -590.0, 288.0, -3793.0, -3934.0, -830.0, 564.0, -1103.0, -5270.0, 121.0, 950.0, -2570.0, -502.0, -1556.0, -142.0, -1683.0, -2455.0, -3154.0, -2773.0, -2883.0, -1375.0, -2866.0, -5988.0, 1914.0, -2311.0, -1654.0, -2757.0, -4321.0, -29329.0, 26384.0, 2636.0, -5619.0, -3352.0, -5555.0, -72.0, -5429.0, -751.0, -2445.0, -8749.0, -4021.0, -912.0, -2294.0, 6468.0, 135.0, 1281.0, -2321.0, -320.0, -2578.0, -3737.0, -1470.0, -1841.0, -631.0, -1108.0, -2371.0, -2055.0, -3166.0, -1419.0, -677.0, -3666.0, -881.0, -20.0, -4403.0, 1366.0, -3804.0, 1064.0, -10377.0, 4307.0, -3898.0, -845.0, 3795.0, -7509.0, -21636.0, 12672.0, 9857.0, -2862.0, -4136.0, -1805.0, -5989.0, 410.0, 1048.0, -13174.0, -949.0, -3802.0, -4939.0, 1437.0, -506.0, 1305.0, 6104.0, -1481.0, -3925.0, 1949.0, -1001.0, -4920.0, -172.0, -1043.0, -1158.0, -2925.0, -994.0, -2615.0, 720.0, -8393.0, 3785.0, -3428.0, -7614.0, 5963.0, -1540.0, -4688.0, -722.0, 881.0, -4912.0, 2058.0, -493.0, -7200.0, 4413.0, -34168.0, 29170.0, 1335.0, -4874.0, -13611.0, 8360.0, -4880.0, 1229.0, -4077.0, -7090.0, 4488.0, -8641.0, -3558.0, -2288.0, 3415.0, -1972.0, 4252.0, -578.0, -2509.0, -1106.0, -297.0, -3186.0, 1630.0, -5392.0, 261.0, -446.0, -12592.0, 10760.0, -3906.0, -3190.0, -2114.0, -1968.0, 880.0, 883.0, -3583.0, -4262.0, -4495.0, 505.0, 2194.0, -469.0, -5780.0, 5805.0, -11440.0, -21706.0, 27385.0, -8533.0, 2782.0, 362.0, -5929.0, -1915.0, -4238.0, 1071.0, -8529.0, 2317.0, -7595.0, -5143.0, 240.0, 6792.0, -2586.0, 5445.0, -2862.0, -3263.0, -4361.0, 3596.0, -3985.0, -438.0, -1449.0, -2594.0, 627.0, -3802.0, 1196.0, -2165.0, 319.0, -4753.0, -5308.0, 3199.0, -3945.0, -2982.0, 850.0, -1623.0, -2724.0, -828.0, -3097.0, -6728.0, 4599.0, 1662.0, -6493.0, 2834.0, -35656.0, 20133.0, 12750.0, -7834.0, -1832.0, 172.0, -11288.0, 13703.0, -12787.0, -6303.0, -2303.0, -2038.0, -7853.0, 8006.0, 707.0, -811.0, 3311.0, -2042.0, -1985.0, -423.0, -2754.0, 335.0, -5464.0, 600.0, -3398.0, -866.0, -1193.0, -2135.0, -2609.0, 1194.0, -2424.0, -2590.0, -3526.0, 790.0, -5170.0, 5491.0, 51.0, -14384.0, 9287.0, -4215.0, -7155.0, 9432.0, -12910.0, -1309.0, 5215.0, -3607.0, -6808.0, 9298.0, -22541.0, -12006.0, 28921.0, -9387.0, -1677.0, -656.0, -4015.0, -998.0, -1964.0, -5664.0, -4743.0, -3378.0, -9891.0, 6259.0, -585.0, 3174.0, -315.0, -507.0, -132.0, -463.0, -2709.0, -1921.0, -2463.0, -2316.0, 455.0, -2531.0

这是FFT值：

850159, 149286, 265943, 245545, 268816, 273358, 259215, 258683, 247526, 273654, 242403, 281878, 307284, 278415, 271214, 258875, 253768, 252473, 255385, 220324, 231414, 242633, 226099, 191531, 248391, 171515, 218672, 186567, 214938, 224413, 216581, 235749, 186375, 164166, 44581, 278924, 93980, 175930, 178638, 154459, 170033, 192662, 140531, 132274, 128717, 119741, 260519, 78757, 246641, 188627, 160756, 119053, 131311, 98181, 100447, 111493, 168179, 130609, 95353, 186940, 109973, 110107, 97234, 140556, 196081, 214005, 135410, 35912, 141008, 138413, 52177, 175686, 129286, 90057, 164437, 186183, 188454, 219768, 101066, 182511, 147675, 20046, 328759, 143892, 75628, 127744, 111484, 255969, 211560, 3946, 82988, 207029, 98322, 130963, 168633, 122201, 38624, 340126, 168085, 115223, 37400, 94940, 85540, 108631, 51006, 197575, 146065, 51800, 239245, 67848, 263602, 69630, 78250, 125533, 164151, 215253, 147920, 208686, 64569, 229339, 93518, 260792, 39166, 125931, 242542, 48721, 174348, 141559, 125815, 78765, 79803, 270542, 135343, 89293, 167074, 111937, 130130, 23251, 220470, 144755, 83364, 59643, 263924, 81461, 146219, 101076, 98141, 100952, 145975, 170965, 107258, 24782, 164298, 133108, 153683, 96266, 184367, 252932, 66484, 150744, 140932, 48479, 196921, 85676, 117759, 220018, 87578, 204263, 406546, 205701, 153631, 329187, 232988, 75216, 88677, 77744, 201402, 237572, 39696, 254693, 423076, 393125, 318252, 98043, 212493, 70255, 3664, 148288, 81766, 31081, 173588, 262050, 240517, 72926, 194867, 166347, 41535, 163457, 90379, 27538, 87297, 161587, 182472, 36915, 262205, 199485, 215211, 87933, 59445, 76130, 66797, 263300, 108378, 205190, 221071, 272146, 213902, 125151, 171001, 44875, 107620, 118709, 32582, 17918, 91632, 166583, 131732, 270558, 152837, 146896, 61740, 39048, 180589, 208806, 163988, 130691, 186421, 88166, 331794, 293086, 188767, 104598, 61049, 66532, 92698, 172981, 51492, 144210, 96422, 146135, 143004, 337824, 130458, 91313, 137682, 112294, 263795, 112294, 137682, 91313, 130458, 337824, 143004, 146135, 96422, 144210, 51492, 172981, 92698, 66532, 61049, 104598, 188767, 293086, 331794, 88166, 186421, 130691, 163988, 208806, 180589, 39048, 61740, 146896, 152837, 270558, 131732, 166583, 91632, 17918, 32582, 118709, 107620, 44875, 171001, 125151, 213902, 272146, 221071, 205190, 108378, 263300, 66797, 76130, 59445, 87933, 215211, 199485, 262205, 36915, 182472, 161587, 87297, 27538, 90379, 163457, 41535, 166347, 194867, 72926, 240517, 262050, 173588, 31081, 81766, 148288, 3664, 70255, 212493, 98043, 318252, 393125, 423076, 254693, 39696, 237572, 201402, 77744, 88677, 75216, 232988, 329187, 153631, 205701, 406546, 204263, 87578, 220018, 117759, 85676, 196921, 48479, 140932, 150744, 66484, 252932, 184367, 96266, 153683, 133108, 164298, 24782, 107258, 170965, 145975, 100952, 98141, 101076, 146219, 81461, 263924, 59643, 83364, 144755, 220470, 23251, 130130, 111937, 167074, 89293, 135343, 270542, 79803, 78765, 125815, 141559, 174348, 48721, 242542, 125931, 39166, 260792, 93518, 229339, 64569, 208686, 147920, 215253, 164151, 125533, 78250, 69630, 263602, 67848, 239245, 51800, 146065, 197575, 51006, 108631, 85540, 94940, 37400, 115223, 168085, 340126, 38624, 122201, 168633, 130963, 98322, 207029, 82988, 3946, 211560, 255969, 111484, 127744, 75628, 143892, 328759, 20046, 147675, 182511, 101066, 219768, 188454, 186183, 164437, 90057, 129286, 175686, 52177, 138413, 141008, 35912, 135410, 214005, 196081, 140556, 97234, 110107, 109973, 186940, 95353, 130609, 168179, 111493, 100447, 98181, 131311, 119053, 160756, 188627, 246641, 78757, 260519, 119741, 128717, 132274, 140531, 192662, 170033, 154459, 178638, 175930, 93980, 278924, 44581, 164166, 186375, 235749, 216581, 224413, 214938, 186567, 218672, 171515, 248391, 191531, 226099, 242633, 231414, 220324, 255385, 252473, 253768, 258875, 271214, 278415, 307284, 281878, 242403, 273654, 247526, 258683, 259215, 273358, 268816, 245545, 265943

这些价值观仍然相去甚远。在我的另一只手腕上，我有一个单独的可穿戴设备，它跟踪我的心率，对于给定的样本，它报告的心率为77bpm

---

更新3-用于测试正常运行的FFT（稍后将在Octive中测试）。但是，我不确定我是否正确处理了数据。我会继续玩这个，看看我是否能改善结果

这是频谱图：

这是我的密码：

Fs = 50;                    % Sampling frequency
T = 1/Fs;                     % Sample time
L = 476;                     % Length of signal
t = (0:L-1)*T;                % Time vector
% Sum of a 50 Hz sinusoid and a 120 Hz sinusoid
y = [ -70756 -56465 -52389 -25199 -20352 -13660 -12615 -9202 -10225 -6168 -5338 4409 -1204 3009 1821 -3127 2076 720 675 -880 622 1851 -915 1296 -3069 -10 1114 2335 -4363 3386 -189 -2497 6326 -4007 -2708 1120 -2159 2643 -1817 749 6096 -2927 -1514 -24006 18897 10851 -2934 -1487 -1660 90 1999 -4448 2567 -1185 -2172 -4479 -253 5173 5956 2814 3279 1617 5174 -4152 911 2404 1579 792 573 -28 3251 159 -2170 727 2652 -2676 3039 -2938 2539 1586 -1447 132 -60 439 -87 -2239 2074 1268 -3559 1266 -18937 -869 25032 -6298 -1653 590 -1737 -3840 -484 -3408 -2470 -3663 -1526 -158 -748 5249 -44 1903 -1900 2513 -58 -2065 -450 -1131 -2262 3663 -2968 1262 -1687 -2745 -581 -11 -528 349 -2231 -1198 -2039 1362 -3671 580 -794 -3924 -1711 2093 -935 2423 -1017 -5674 -26830 27284 4433 -4604 -2655 -4541 -2643 2036 -3159 -3194 -2030 -2535 -5753 -31 5056 241 4452 -1591 -1056 573 -3637 -1224 -2728 3535 -2645 -1281 -1359 -1918 621 -2967 2535 -3048 -2820 -2530 -1202 315 -645 -3541 -3547 -2725 -4590 -124 620 -1866 -4450 -17536 4480 16119 -7421 2363 -8373 3109 -896 -6533 -1502 -378 -3602 -5893 -2730 2619 3532 675 -778 -590 288 -3793 -3934 -830 564 -1103 -5270 121 950 -2570 -502 -1556 -142 -1683 -2455 -3154 -2773 -2883 -1375 -2866 -5988 1914 -2311 -1654 -2757 -4321 -29329 26384 2636 -5619 -3352 -5555 -72 -5429 -751 -2445 -8749 -4021 -912 -2294 6468 135 1281 -2321 -320 -2578 -3737 -1470 -1841 -631 -1108 -2371 -2055 -3166 -1419 -677 -3666 -881 -20 -4403 1366 -3804 1064 -10377 4307 -3898 -845 3795 -7509 -21636 12672 9857 -2862 -4136 -1805 -5989 410 1048 -13174 -949 -3802 -4939 1437 -506 1305 6104 -1481 -3925 1949 -1001 -4920 -172 -1043 -1158 -2925 -994 -2615 720 -8393 3785 -3428 -7614 5963 -1540 -4688 -722 881 -4912 2058 -493 -7200 4413 -34168 29170 1335 -4874 -13611 8360 -4880 1229 -4077 -7090 4488 -8641 -3558 -2288 3415 -1972 4252 -578 -2509 -1106 -297 -3186 1630 -5392 261 -446 -12592 10760 -3906 -3190 -2114 -1968 880 883 -3583 -4262 -4495 505 2194 -469 -5780 5805 -11440 -21706 27385 -8533 2782 362 -5929 -1915 -4238 1071 -8529 2317 -7595 -5143 240 6792 -2586 5445 -2862 -3263 -4361 3596 -3985 -438 -1449 -2594 627 -3802 1196 -2165 319 -4753 -5308 3199 -3945 -2982 850 -1623 -2724 -828 -3097 -6728 4599 1662 -6493 2834 -35656 20133 12750 -7834 -1832 172 -11288 13703 -12787 -6303 -2303 -2038 -7853 8006 707 -811 3311 -2042 -1985 -423 -2754 335 -5464 600 -3398 -866 -1193 -2135 -2609 1194 -2424 -2590 -3526 790 -5170 5491 51 -14384 9287 -4215 -7155 9432 -12910 -1309 5215 -3607 -6808 9298 -22541 -12006 28921 -9387 -1677 -656 -4015 -998 -1964 -5664 -4743 -3378 -9891 6259 -585 3174 -315 -507 -132 -463 -2709 -1921 -2463 -2316 455 -2531.0 ] % Sinusoids plus noise

NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT);
Pyy = Y.*conj(Y)/L;


plot(Pyy(1:238))
title('Power spectral density')
xlabel('Frequency (Hz)')

---

更新4-决定尝试不同的方法。在这种情况下，使用自相关、低通滤波和FFT

首先是自相关：如果数据中的噪声最小，结果就相当准确。但是，一旦出现噪音，结果就不再可靠。代码如下：

private float correlate(List<Float> data, int nElements, int offset)
{
    float sum = 0;

    for(int i = 0; i < nElements - offset; i++)
    {
        sum += data.get(i) * data.get(i + offset);
    }
    return sum;
}

int getBeat(List<Float> data, int n)
{
    int minEle = 0, maxEle, i;
    float minVal, maxVal;

    List<Float> correlatedValues = new ArrayList<>();

    for(i = 0; i < n; i++)
    {
        correlatedValues.add(correlate(data, n, i));
    }

    minVal = correlatedValues.get(0);

    for(i = 1; i < n; i++)
    {
        if(correlatedValues.get(i) > correlatedValues.get(i - 1))
        {
            minVal = correlatedValues.get(i);
            minEle = i;
            break;
        }
    }

    maxVal = minVal;
    maxEle = minEle;
    for (i=minEle; i<n; i++)
    {
        if (correlatedValues.get(i) > maxVal)
        {
            maxVal = correlatedValues.get(i);
            maxEle = i;
        }
    }

    return maxEle;
}

private float correlate（列表数据、整数元素、整数偏移量）
{
浮点数和=0；
对于（int i=0；icorrelatedValues.get（i-1））
{
minVal=correlatedValues.get（i）；
minEle=i；
打破
}
}
maxVal=minVal；
maxEle=minEle；
for（i=minEle；i maxVal）
{
maxVal=correlatedValues.get（i）；
maxEle=i；
}
}
返回maxEle；
}

返回的结果是拍之间的距离。将样本长度除以距离得到样本的心率。示例：470（样本量）/46（距离）=10（每10秒样本的拍数）*6=60Bpm

如前所述，噪声掩盖了这一点，所以我试图拼凑一个基于噪声的低通滤波器。下面是我想到的代码：

private List<Float> lowPassFilter(List<Float> frequencies, float smoothing)
{
    float frequency = frequencies.get(0);
    for(int i  = 1; i < frequencies.size(); i++)
    {
        float currentFrequency = frequencies.get(i);
        frequency += (currentFrequency - frequency) / smoothing;
        frequencies.set(i, frequency);
    }
    return frequencies;
}

私有列表低通滤波器（列表频率、浮点平滑）
{
浮动频率=频率。获取（0）；
对于（int i=1；i

问题是，无论我通过什么运行低通滤波器的结果（自相关、Chauvenet准则或峰值搜索），结果都是0（零）。我的猜测是，我的过滤器实现是关闭的

然而，我也尝试使用FFT来获得频率，然后使用这些结果进行自动相关，结果仍然是0（零）。以下是使用FFT获取频率的代码：

    private List<Float> fft(List<Integer> ecgValues, TransformType transformType)
{
    int samplingFrequency = 50;

    List<Integer> transformedStream = new ArrayList<>();

    FastFourierTransformer ffs = new FastFourierTransformer(DftNormalization.STANDARD);
    double[] input = convertIntegerListToDoubleArray(ecgValues);

    Complex[] complex = ffs.transform(input, transformType);

    List<Float> magnitude = calculatePowerSpectrum(complex);

    List<Float> frequencies = powerSpectrumToFrequency(magnitude, samplingFrequency, ecgValues.size());

    return frequencies;
}

private List<Float> calculatePowerSpectrum(Complex[] complex)
{
    List<Float> magnitude = new ArrayList<>();

    for(int i = 0; i < complex.length - 1; i++)
    {
        double real = (complex[i].getReal());
        double imaginary = (complex[i].getImaginary());

        magnitude.add((float) Math.sqrt((real * real) + (imaginary * imaginary)));

    }

    return magnitude;
}

私有列表fft（列表ecgValues，TransformType）
{
int
private List<Float> lowPassFilter(List<Float> frequencies, float smoothing)
{
    float frequency = frequencies.get(0);
    for(int i  = 1; i < frequencies.size(); i++)
    {
        float currentFrequency = frequencies.get(i);
        frequency += (currentFrequency - frequency) / smoothing;
        frequencies.set(i, frequency);
    }
    return frequencies;
}

    private List<Float> fft(List<Integer> ecgValues, TransformType transformType)
{
    int samplingFrequency = 50;

    List<Integer> transformedStream = new ArrayList<>();

    FastFourierTransformer ffs = new FastFourierTransformer(DftNormalization.STANDARD);
    double[] input = convertIntegerListToDoubleArray(ecgValues);

    Complex[] complex = ffs.transform(input, transformType);

    List<Float> magnitude = calculatePowerSpectrum(complex);

    List<Float> frequencies = powerSpectrumToFrequency(magnitude, samplingFrequency, ecgValues.size());

    return frequencies;
}

private List<Float> calculatePowerSpectrum(Complex[] complex)
{
    List<Float> magnitude = new ArrayList<>();

    for(int i = 0; i < complex.length - 1; i++)
    {
        double real = (complex[i].getReal());
        double imaginary = (complex[i].getImaginary());

        magnitude.add((float) Math.sqrt((real * real) + (imaginary * imaginary)));

    }

    return magnitude;
}

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>

static float timeseries1[] =
{
-59752, -66222, -45702, -34272, -25891, -19203, -13547, -12212, -5916, -8793, -5083, -2075, 3231, 6295, 4898, 3029, 3427, 2161, 4274, -1209, 3428, -1793, 2560, 5195, 1092, 8088, 7539, 6673, 7338, 8527, 11586, 12264, 7979, 4316, 8383, 3198, 2555, 3574, 753, 2964, -3042, 901, -3218, -6178, -21116, 24346, -602, -1520, -3454, -1430, -7914, -1906, -6920, -8216, -8013, -6836, -7863, -1031, 3049, -271, -1010, 1562, -166, -1069, 1143, 3268, -1074, -258, -749, 433, -450, 2612, -2582, 1063, -2656, 3751, -1608, 637, -997, -7, 1155, -556, -1397, 2807, -967, 2946, 1198, -1133, -11066, 5439, 11159, -1066, 643, -34, 441, 1378, 1451, -1664, -2054, -2390, -1484, -1227, 5589, 5151, 4068, 3040, -2243, 1762, -2942, 51, 1793, 245, 171, 639, -375, 1296, -1327, 729, -624, -2642, 3964, -2641, 286, -2766, -393, -316, 2343, -3658, -552, 613, 2687, -1347, 539, -11251, 2873, 14529, -5234, -919, -2486, -3641, 4647, 0, -2149, -4063, -2619, -749, 18, 5274, 6670, 1413, 2697, 2673, 157, -180, 166, 2352, 454, 2013, -2867, 3788, -423, 1680, 1167, -1282, 1554, 768, 298, 205, -480, 2618, 531, -839, -1067, -1056, 1693, 3300, 52, -2087, 259, -5031, -4896, 15720, -3576, -3005, 849, -2643, 2204, -4461, -1953, -572, -3743, -3664, -2254, 3326, 7791, 2388, -1847, 2592, -1142, -1550, 1224, -1044, -1698, -481, 1469, -479, -125, -1853, 455, -38, 167, -55, -2126, -2291, 96, 1179, -2948, -1960, -876, 29, -2660, 1465, -1025, -2131, 2058, -3111, -19865, 20644, 1786, -2853, -2190, -2047, -1873, -643, -921, -3191, -3524, -5160, -3216, 2431, 7117, 1796, 2435, -516, 1557, -1248, -2745, -860, -618, -565, -93, 602, -3364, -1658, 1398, -126, -1715, -1685, 680, -1805, 232, -2093, -1703, -2844, -628, -2049, -1450, 1737, -1216, 2681, -2963, -4605, -11062, 15109, 133, -3804, -2971, -1867, -194, -1433, -4328, -2887, -4452, -3241, -1997, 1815, 6139, 1655, 1583, 520, -2574, -2458, 299, -2345, -475, 991, -2273, -1038, -154, 267, -1528, -1720, -440, -77, -1717, -28, -2684, -606, -1862, -560, -2120, -900, -4206, 2636, -8, -917, -1249, -3586, -13119, 8999, 6520, -2474, -3229, -1804, -1933, -1104, -3035, -1307, -3457, -4996, -2804, -2841, 3889, 6843, 1992, -671, 548, -1871, -2000, 1441, -1519, -2303, -1067, 1131, -1001, -1396, -289, -968, 1864, -3006, -1918, -72, -239, -589, -2233, -1982, 2608, -2765, -1461, -2215, -1916, 2924, -13, 342, -446, -3427, -19378, 20846, 2310, -6999, -1806, -728, -932, -2081, -2129, -2054, -4103, -2641, -4826, 1457, 3338, 6764, 2363, -1811, 453, -2577, -796, -237, -663, -1594, -170, -922, -149, -2258, -816, -1250, -1640, 2522, -4363, 668, -3494, -557, -21, -263, -4197, 694, -2921, -161, -3000, -852, 3120, 339, -1138, -2066, -4505, -13751, 17435, -446, -4212, -1339, -2239, -223, -1322, -3550, -3987, -2102, -3505, -3971, 3695, 3535, 3150, 2459, 1575, -3297, -383, -1470, 1556, -2191, -123, -1444, -1572, 1973, -3773, 1206, -860, -1384, -395, -818, -934, -940, -494, 795, -1416, -3613, -442, 622, -2798, 1296, -373, -400, -1270, 278, -5536, -14798, 20071, -2973, -3795, -754, -3358, -393, -2279, -1834, -1983, -5568, -4118, -2595, 1443, 6367, 3245, 1500, -1697, 1287
};


static float timeseries2[] =
{
-35751, -32565, -28033, -23493, -18135, -10310, -8731, -4143, -5485, -2162, -955, -6393, -4211, -3047, -3097, -3232, -2975, -1571, -2105, -1440, -3880, -372, -227, -1266, -2269, -299, 2255, -2534, -3677, 675, 78, 415, -2274, -2256, 875, -13756, -5896, 15991, 585, -4356, 2706,
-2028, 2127, -2249, -1282, -2555, -2865, -2570, -2666, 3745, 5965, 2728, -73, 611, 342, 1297, 214, -1153, 496, -283, -1868, 1791, -541, 2044, -414, 1595, 72, -2262, -363, 1855, -649, 909, -815, -363, 2791, 152, 1072, -2025, 1291, -12311, -6729, 22739, -4036, -784, 2598, -871,
-2182, 1244, -2158, -2403, -1551, -3825, -4385, 4281, 5919, 6609, -2120, 480, 1070, -736, 525, -1520, -2225, 1795, 574, 781, -584, -1750, 175, 3339, -1175, 1186, -1319, 361, 885, -46, -1078, -2569, -720, 1533, 2465, 113, -1953, 2475, -5732, -22272, 24177, 235, 1385, -3850, 2291, -1417, -2452, -862, -3745, -932, -3586, -3987, -69, 5431, 3902, 2284, -619, 609, -1424, -1467, -1055, -1166, -1216, 1515, -1851,
-49, -4983, 1495, 3563, -873, -1933, -397, -933, 546, -1925, -753, -53, -2603, -591, 769, 3005, -2773, 2097, -5993, -21911, 23700, 3747, -4986, 595, -1815, -1589, -571, -2116, -1823, -6708, -1686, -1891, -991, 5178, 3719, 1188, -2394, 3992, -1555, -5306, 2830, 25, -2564, 2112, -1723, -3810, 4700, -2780, 520, -70, -2015, 1093, -2231, 2526,
-4651, -799, 764, -2429, 272, -564, 1119, -1089, 2371, -5627, -8118, 7574, 6499, -8635, 582, -2186, -1986, -477, -2178, -707, -6743, -3582,
-4409, 1806, 2718, 5820, -272, 1046, -580, -1552, -1184, -3206, -690, 1218, -871, -1919, -2552, 2127, -754, -1848, -3573, 3112, -1170, 468,
-2593, -382, -3280, 3664, -5572, 1992, -30, -7230, 8670, -2504, -4969, -14813, 225, 14109, 8194, -9438, -4781, 3102, -8626, 6428, -5387, -5050, 548, -10060, 6965, -2155, 2195, 5498, 359, -4090, 5130, -4214, 1478, -364, -6444, 5889, -3363, -1621, -3570, 8390, -5828, -1472, 841,
-8869, 11057, -6734, 173, 535, -638, -2628, -2751, 4754, 514, -2423, 1168, -3860, -23875, 18070, 7511, -3048, -1173, -6033, 5087, -5258,
-3012, -831, -1180, -5298, -557, -2993, 6236, 1417, 2683, 361, 2293, -4117, 1122, -1922, -3730, 2705, -848, -3560, 2100, -319, -495, -347, -2329, 1341, -805, 1227, -2463, -440, -1440, 1206, -2361, -411, -1481, 3837, -3101, 1851, -5779, -22183, 22335, 3443, -3854, -2077, -2311, 1471, -817, 792, -7227, -2963, -4038, -92, -1234, 4692, 3973, 2122, 1333, -222, -2997, 1279, -3531, 1335, 140, -375, -2235, 2795, 598,
-3233, -951, 1895, -288, -925, 1066, -3400, -1230, -2011, 2217, 1942, -1790, -1700, -1450, 756, -10710, -6744, 18590, -1435, -1739, -2097, -2638, -454, 67, -4556, -695, -5602, -2815, -2142, 764, 5958, 2175, 2055, -647, -466, -478, -1082, 527, -2214, 275, 274, -1687, -2358, 31, 1570, -1587, -871, -271, -2365, 1337, -831, -1095, -2056, -208, -1383, 2415, -1523, -1538, -719, -3842, -20933, 15223, 9978, -4030, -2521, 190, -4163, -2305, 1814, -2465, -4207, -3792, -2559, -2123, 2908, 5366, 2933, -1455, -57, 112, -2241, -1416, -2778, 2353, -1200, -2027,
-962, 1117, -1530, 157, -2902, 3466, -5072, 555, 1425, -2791, -1369, 156, -6789, 1961, -1111, 3631, -2592, -1643, 2039, -2865
};


float correlate (float * data, int nElements, int offset)
/////////////////////////////////////////////////////////
{
  float summ = 0;
  int i;

  for (i=0; i<nElements - offset; i++)
    summ += data[i] * data[(i+offset)];

  return summ;
}


int getBeat (float * data, int n)
/////////////////////////////////
{
  float * c = (float *) malloc (n * sizeof (float));

  int    minEle, maxEle, i;
  float  minVal, maxVal;

  // calculate the time-delayed correlation of the signal with itself:
  for (i=0; i<n; i++)
    c[i] = correlate (data, n, i);

  // Heuristic: Search for the first element that is higher than
  // it's precursor: (this is an heuristic to skip the trivial
  // correlation of the signal with itself).
  minVal = c[0];
  for (i=1; i<n; i++)
  {
    if (c[i] > c[i-1])
    {
      minVal = c[i];
      minEle = i;
      break;
    }
  }

  // Now just search for the highest peak. That's
  // where the highest periodicity in the signal is
  // located:
  maxVal = minVal;
  maxEle = minEle;
  for (i=minEle; i<n; i++)
  {
    if (c[i] > maxVal)
    {
      maxVal = c[i];
      maxEle = i;
    }
  }
  free (c);

  return maxEle;
}


int main (int argc, char **args)
{
  int nElements1 = sizeof (timeseries1) / sizeof (float);
  int nElements2 = sizeof (timeseries2) / sizeof (float);

  printf ("beat distance is %d samples\n",
    getBeat (timeseries1, nElements1));

  printf ("beat distance is %d samples\n",
    getBeat (timeseries2, nElements2));
  return 1;
}

beat distance is 46 samples
beat distance is 45 samples