女士们，先生们，请让我再次为您解决我的问题。在下面的程序中，只有一个频率为 256 Hz、幅度为 100,000、相位为 0.67 pi rad 的正弦曲线。测试频率网格为 1 Hz 步长，从 0 Hz 到 1000 Hz。输出在 256 Hz 时的最大幅度为 99,221，相位为 0.670561 pi rad。考虑到准确性的错误，我认为这没问题。

但是伪频率幅度有起有落，而我对 DFT 的理解是它们应该上升到 256 Hz 然后下降。为什么会有这些起伏？我仍然问候。

// Grid is created by variables lowTestFreq and testFreqStep
// both of double type, and integer type M.
// In comments are units of variables.

#include <iostream>
#include "math.h"

int main()
{  
    //Unchanged variables.
    double pi = 3.141592653589793; //pure number.
    int n = 0; // sample.
    double xn = 0; //pure number.
    double Re = 0; //pure number.
    double Im = 0; //pure number.
    double xn_cos = 0; //pure number.
    double xn_sin = 0; //pure number.
    double testAmpl = 0; // pure number.
    double testPhase = 0; // rad and then pirad.   

    //Sampling frequency and samples of segment.
    int samplFreq = 50000; // sample/second.
    int N = 3000; //sample.

    // Existing sinusoid.
    double ampl_1 = 100000; //pure number.
    double existFreq_1 = 256; // Hz.
    double phase_1 = 0.67 * pi; // rad.
    double unitAngle_1 = (existFreq_1 / samplFreq) * (2 * pi); // rad/sample.

    // Testing grid.
    double testFreq = 0; // Hz.
    double testUnitAngle = 0; // rad.
    double testAngle = 0; // 
    double lowTestFreq = 0; //Hz.
    double testFreqStep = 1; // Hz.
    int M = 1000; // pure number.
    int m = 0; // pure number.

    for (m = 0; m <= M; ++m)
    {
        testFreq = lowTestFreq + (m * testFreqStep); // Hz.
        testUnitAngle = (testFreq / samplFreq) * (2 * pi); // rad/sample.

        Re = 0; Im = 0;

        for (n = 1; n <= N; ++n)
        {
            xn = ampl_1 * sin(n * unitAngle_1 + phase_1);

            testAngle = n * testUnitAngle;
            xn_cos = xn *  cos(testAngle);
            xn_sin = xn * -sin(testAngle);

            Re += xn_cos;
            Im += xn_sin;
        }  
        std::cout << "Test Freq " << testFreq; // Hz.
        testAmpl = sqrt(Re * Re + Im * Im) / N * 2; //pure number.       
        std::cout << "       Test Freq's Ampl: " << testAmpl;
        testPhase = atan2 (Im, Re); // rad.
        testPhase = testPhase / pi; // pirad.
        testPhase = testPhase + 0.5; // pirad. Corrected phase.
        std::cout << ",    and its phase: " << testPhase 
            << " pirad." << std::endl;
    }       
    return 0;
}