Perform the DCT in C++

main.cpp

 #include <Eigen/Core>
 #include <iostream>
 
+//--------------------------------------------------------------------------------------------------
 using Scalar = double;
 using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
 using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
 
+//--------------------------------------------------------------------------------------------------
+constexpr Scalar pi = 3.1415926535897932384626433832795;
+
+//--------------------------------------------------------------------------------------------------
 void python_print(char const* name, Vector const& x) {
     std::cout << name << " = np.array([";
     std::cout << x[0];
@@ -14,23 +19,49 @@ void python_print(char const* name, Vector const& x) {
     std::cout << "])\n";
 }
 
+//--------------------------------------------------------------------------------------------------
+Vector sample_two_sins(Scalar f1, Scalar f2, Vector const& sample_times) {
+    Vector const sample_rads = 2 * pi * sample_times;
+    return sin((f1 * sample_rads).array()) + sin((f2 * sample_rads).array());
+}
+
+//--------------------------------------------------------------------------------------------------
+Matrix compute_dct_matrix(uint32_t n_samples) {
+    Matrix dct_matrix(n_samples, n_samples);
+    Scalar root_one_over_n = std::sqrt(1.0 / n_samples);
+    Scalar root_two_over_n = std::sqrt(2.0 / n_samples);
+    for (uint32_t j = 0; j < n_samples; ++j) {
+        dct_matrix(0, j) = root_one_over_n;
+    }
+    for (uint32_t i = 1; i < n_samples; ++i) {
+        for (uint32_t j = 0; j < n_samples; ++j) {
+            dct_matrix(i, j) = root_two_over_n * cos(pi * (2 * j + 1) * i / (2 * n_samples));
+        }
+    }
+    return dct_matrix;
+}
+
 //--------------------------------------------------------------------------------------------------
 int main() {
     //Vector x = Vector::Random(5);
     //std::cout << x << '\n';
 
-    Scalar pi = 3.1415926535897932384626433832795;
 
     Scalar f1 = 697;
     Scalar f2 = 1209;
 
+    // Part (a)
     Scalar sample_period = 0.01;
-    uint32_t n_samples = 10;
-    Vector sample_times = (sample_period / n_samples) * Vector::LinSpaced(n_samples, 0, n_samples);
+    uint32_t n_samples = 250;
+    Vector const sample_times = (sample_period / n_samples) * Vector::LinSpaced(n_samples, 0, n_samples);
+    Vector const sample_values = sample_two_sins(f1, f2, sample_times);
     python_print("sample_times", sample_times);
-    Vector sample_rads = 2 * pi * sample_times;
-    Vector sample_values = sin((f1 * sample_rads).array()) + sin((f2 * sample_rads).array());
     python_print("sample_values", sample_values);
 
+    // Part (b)
+    Matrix dct_matrix = compute_dct_matrix(n_samples);
+    Vector dct = dct_matrix * sample_values;
+    python_print("dct", dct);
+
     return 0;
 }

plotter.py

 import numpy as np
 import matplotlib.pyplot as plt
 
+sample_times = np.array([0, 4.01606e-05, 8.03213e-05, 0.000120482, 0.000160643, 0.000200803, 0.000240964, 0.000281124, 0.000321285, 0.000361446, 0.000401606, 0.000441767, 0.000481928, 0.000522088, 0.000562249, 0.00060241, 0.00064257, 0.000682731, 0.000722892, 0.000763052, 0.000803213, 0.000843373, 0.000883534, 0.000923695, 0.000963855, 0.00100402, 0.00104418, 0.00108434, 0.0011245, 0.00116466, 0.00120482, 0.00124498, 0.00128514, 0.0013253, 0.00136546, 0.00140562, 0.00144578, 0.00148594, 0.0015261, 0.00156627, 0.00160643, 0.00164659, 0.00168675, 0.00172691, 0.00176707, 0.00180723, 0.00184739, 0.00188755, 0.00192771, 0.00196787, 0.00200803, 0.00204819, 0.00208835, 0.00212851, 0.00216867, 0.00220884, 0.002249, 0.00228916, 0.00232932, 0.00236948, 0.00240964, 0.0024498, 0.00248996, 0.00253012, 0.00257028, 0.00261044, 0.0026506, 0.00269076, 0.00273092, 0.00277108, 0.00281124, 0.00285141, 0.00289157, 0.00293173, 0.00297189, 0.00301205, 0.00305221, 0.00309237, 0.00313253, 0.00317269, 0.00321285, 0.00325301, 0.00329317, 0.00333333, 0.00337349, 0.00341365, 0.00345382, 0.00349398, 0.00353414, 0.0035743, 0.00361446, 0.00365462, 0.00369478, 0.00373494, 0.0037751, 0.00381526, 0.00385542, 0.00389558, 0.00393574, 0.0039759, 0.00401606, 0.00405622, 0.00409639, 0.00413655, 0.00417671, 0.00421687, 0.00425703, 0.00429719, 0.00433735, 0.00437751, 0.00441767, 0.00445783, 0.00449799, 0.00453815, 0.00457831, 0.00461847, 0.00465863, 0.0046988, 0.00473896, 0.00477912, 0.00481928, 0.00485944, 0.0048996, 0.00493976, 0.00497992, 0.00502008, 0.00506024, 0.0051004, 0.00514056, 0.00518072, 0.00522088, 0.00526104, 0.0053012, 0.00534137, 0.00538153, 0.00542169, 0.00546185, 0.00550201, 0.00554217, 0.00558233, 0.00562249, 0.00566265, 0.00570281, 0.00574297, 0.00578313, 0.00582329, 0.00586345, 0.00590361, 0.00594378, 0.00598394, 0.0060241, 0.00606426, 0.00610442, 0.00614458, 0.00618474, 0.0062249, 0.00626506, 0.00630522, 0.00634538, 0.00638554, 0.0064257, 0.00646586, 0.00650602, 0.00654618, 0.00658635, 0.00662651, 0.00666667, 0.00670683, 0.00674699, 0.00678715, 0.00682731, 0.00686747, 0.00690763, 0.00694779, 0.00698795, 0.00702811, 0.00706827, 0.00710843, 0.00714859, 0.00718876, 0.00722892, 0.00726908, 0.00730924, 0.0073494, 0.00738956, 0.00742972, 0.00746988, 0.00751004, 0.0075502, 0.00759036, 0.00763052, 0.00767068, 0.00771084, 0.007751, 0.00779116, 0.00783133, 0.00787149, 0.00791165, 0.00795181, 0.00799197, 0.00803213, 0.00807229, 0.00811245, 0.00815261, 0.00819277, 0.00823293, 0.00827309, 0.00831325, 0.00835341, 0.00839357, 0.00843373, 0.0084739, 0.00851406, 0.00855422, 0.00859438, 0.00863454, 0.0086747, 0.00871486, 0.00875502, 0.00879518, 0.00883534, 0.0088755, 0.00891566, 0.00895582, 0.00899598, 0.00903614, 0.00907631, 0.00911647, 0.00915663, 0.00919679, 0.00923695, 0.00927711, 0.00931727, 0.00935743, 0.00939759, 0.00943775, 0.00947791, 0.00951807, 0.00955823, 0.00959839, 0.00963855, 0.00967871, 0.00971888, 0.00975904, 0.0097992, 0.00983936, 0.00987952, 0.00991968, 0.00995984, 0.01])
+sample_values = np.array([0, 0.475338, 0.917539, 1.29619, 1.5861, 1.76932, 1.83651, 1.78761, 1.6316, 1.38558, 1.0731, 0.721928, 0.361558, 0.0205522, -0.27594, -0.508314, -0.664077, -0.738727, -0.735864, -0.666533, -0.547871, -0.401193, -0.249706, -0.116065, -0.0200166, 0.0236569, 0.00668195, -0.0718098, -0.205127, -0.379618, -0.575975, -0.771114, -0.94046, -1.06042, -1.1108, -1.07697, -0.951487, -0.73516, -0.43726, -0.0750177, 0.327653, 0.742071, 1.13718, 1.48217, 1.7492, 1.91577, 1.96681, 1.89599, 1.70642, 1.41042, 1.02857, 0.588008, 0.120163, -0.341839, -0.765935, -1.12376, -1.39294, -1.5588, -1.61544, -1.56598, -1.42199, -1.20225, -0.930797, -0.634626, -0.341124, -0.0755387, 0.141293, 0.294754, 0.377636, 0.390584, 0.341783, 0.245913, 0.122481, -0.00631234, -0.117955, -0.19203, -0.212412, -0.169044, -0.0591181, 0.112454, 0.333336, 0.584794, 0.843377, 1.08309, 1.27787, 1.40408, 1.44291, 1.38232, 1.21838, 0.95598, 0.608661, 0.197701, -0.249515, -0.701696, -1.12623, -1.49192, -1.77159, -1.94442, -1.99773, -1.92798, -1.74113, -1.45207, -1.08332, -0.663067, -0.222778, 0.205515, 0.591886, 0.910992, 1.14409, 1.28044, 1.31795, 1.26307, 1.12989, 0.938508, 0.713012, 0.478999, 0.261091, 0.0805585, -0.0466774, -0.11149, -0.112311, -0.0551393, 0.0472029, 0.176484, 0.311019, 0.427974, 0.505792, 0.526522, 0.477802, 0.354329, 0.158647, -0.0988122, -0.400459, -0.722977, -1.03934, -1.32121, -1.54155, -1.67714, -1.71079, -1.63312, -1.44356, -1.15069, -0.771708, -0.33113, 0.14113, 0.6122, 1.04895, 1.42074, 1.70194, 1.87404, 1.9271, 1.86053, 1.68299, 1.41149, 1.06984, 0.686454, 0.291854, -0.0840174, -0.414358, -0.677735, -0.859784, -0.954231, -0.963144, -0.896411, -0.770496, -0.606599, -0.428405, -0.259632, -0.121617, -0.0311657, 0.00112032, -0.0281042, -0.11461, -0.247029, -0.408011, -0.575983, -0.727348, -0.838913, -0.890317, -0.866221, -0.75805, -0.565119, -0.295029, 0.0367266, 0.407896, 0.791266, 1.15696, 1.47502, 1.71807, 1.86376, 1.89685, 1.81066, 1.60779, 1.30007, 0.907671, 0.457475, -0.019091, -0.488655, -0.918654, -1.28001, -1.54948, -1.71149, -1.75931, -1.69539, -1.53092, -1.28466, -0.981105, -0.648113, -0.314394, -0.00689592, 0.25156, 0.444213, 0.561694, 0.602629, 0.573475, 0.487607, 0.363754, 0.223933, 0.0910946, -0.0133094, -0.0715908, -0.0717057, -0.00857246, 0.115302, 0.289952, 0.498828, 0.720336, 0.929905, 1.10238, 1.21454, 1.24743, 1.18842, 1.03264, 0.783761, 0.453978, 0.0632207, -0.36236, -0.792506, -1.19536, -1.54017, -1.79994, -1.95375, -1.9886, -1.9006, -1.69531, -1.38735, -0.999124, -0.559002, -0.0988865, 0.348445])
+dct = np.array([0.0493937, 1.53249, 0.0703373, 1.58311, 0.071832, 1.69718, 0.0744769, 1.91051, 0.0785496, 2.32168, 0.0845789, 3.29439, 0.0938324, 8.09608, -0.948385, -5.98402, 0.120253, -1.12508, 0.152546, 0.119667, 0.214371, 1.22218, 0.385667, 4.39185, 3.03895, -8.90656, -0.469319, -2.524, -0.208824, -1.50006, -0.13078, -1.06566, -0.0934123, -0.821045, -0.0716006, -0.662819, -0.0573687, -0.551709, -0.0473917, -0.469331, -0.0400375, -0.405854, -0.0344114, -0.355506, -0.0299824, -0.314665, -0.0264156, -0.280932, -0.0234894, -0.252653, -0.0210515, -0.228649, -0.0189938, -0.208056, -0.0172374, -0.190227, -0.0157237, -0.174667, -0.0144081, -0.16099, -0.013256, -0.148893, -0.0122403, -0.138131, -0.0113395, -0.128509, -0.0105363, -0.119865, -0.00981652, -0.112068, -0.00916866, -0.105006, -0.00858312, -0.0985874, -0.00805189, -0.092734, -0.00756824, -0.0873795, -0.0071265, -0.0824671, -0.00672179, -0.0779483, -0.00634998, -0.073781, -0.00600749, -0.0699287, -0.00569123, -0.0663596, -0.0053985, -0.0630459, -0.00512696, -0.0599632, -0.00487456, -0.0570899, -0.00463947, -0.0544069, -0.00442012, -0.0518974, -0.00421508, -0.0495463, -0.00402309, -0.0473402, -0.00384303, -0.045267, -0.00367391, -0.0433158, -0.00351482, -0.0414771, -0.00336496, -0.0397421, -0.0032236, -0.0381027, -0.00309008, -0.0365518, -0.00296382, -0.035083, -0.00284426, -0.0336903, -0.00273093, -0.0323682, -0.00262338, -0.0311119, -0.0025212, -0.0299168, -0.00242403, -0.0287789, -0.00233151, -0.0276942, -0.00224334, -0.0266594, -0.00215923, -0.0256711, -0.00207892, -0.0247266, -0.00200217, -0.0238229, -0.00192875, -0.0229577, -0.00185846, -0.0221285, -0.0017911, -0.0213332, -0.0017265, -0.0205698, -0.00166449, -0.0198364, -0.00160493, -0.0191312, -0.00154766, -0.0184527, -0.00149255, -0.0177994, -0.00143949, -0.0171698, -0.00138835, -0.0165626, -0.00133904, -0.0159765, -0.00129144, -0.0154105, -0.00124547, -0.0148635, -0.00120103, -0.0143343, -0.00115805, -0.0138221, -0.00111644, -0.013326, -0.00107613, -0.0128451, -0.00103706, -0.0123786, -0.000999157, -0.0119258, -0.00096236, -0.011486, -0.000926612, -0.0110584, -0.000891859, -0.0106425, -0.000858049, -0.0102376, -0.000825132, -0.00984319, -0.000793062, -0.00945872, -0.000761795, -0.00908367, -0.00073129, -0.00871754, -0.000701505, -0.00835987, -0.000672404, -0.00801022, -0.000643949, -0.00766816, -0.000616107, -0.00733328, -0.000588845, -0.0070052, -0.00056213, -0.00668355, -0.000535933, -0.00636796, -0.000510224, -0.0060581, -0.000484977, -0.00575364, -0.000460163, -0.00545426, -0.000435757, -0.00515967, -0.000411735, -0.00486955, -0.000388072, -0.00458364, -0.000364745, -0.00430165, -0.000341732, -0.00402332, -0.000319012, -0.00374839, -0.000296562, -0.00347661, -0.000274362, -0.00320774, -0.000252393, -0.00294153, -0.000230635, -0.00267776, -0.000209069, -0.00241619, -0.000187676, -0.0021566, -0.000166438, -0.00189878, -0.000145337, -0.00164251, -0.000124355, -0.00138757, -0.000103475, -0.00113376, -8.26789e-05, -0.000880865, -6.19504e-05, -0.000628682, -4.12723e-05, -0.000377007, -2.06278e-05, -0.000125635])
+
 if __name__ == "__main__":
-    sample_times = np.array([0, 0.00111111, 0.00222222, 0.00333333, 0.00444444, 0.00555556, 0.00666667, 0.00777778, 0.00888889, 0.01])
-    sample_values = np.array([0, -0.155307, -1.22423, 1.08309, 1.2909, -1.69749, -0.428405, 1.04634, -0.0577232, 0.348445])
     plt.plot(sample_times, sample_values)
     plt.savefig("fig_a.png")
     plt.close()
+
+    plt.plot(np.arange(len(dct)), dct)
+    plt.savefig("fig_b.png")
+    plt.close()