请让我问你关于 DFT 中的一个现象。下面的 DFT 程序在低采样率下输出出色的结果，但在高采样率下非常糟糕。

具体来说：对于采样率 50 个样本/秒，分段 1000 个样本，现有频率 36.7634 Hz，从 35.2364 Hz 到 40.7896 除以 40 的网格，输出对应于测试频率 36.7635 的最大幅度平方 1.22629e+15。

但是对于 50,000 个样本/秒的采样率，同样分割 1000 个样本，并且现有频率和网格相同，输出对应于测试频率 38.2907 Hz 的最大幅度平方 8.46881e+14。错误为 5 位有效数字。

你知道这种现象吗？如果是，请向我解释一下。

// Grid is created by variables lowTestFreq and highTestFreq
// both of double type, and integer type M.

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

int main()
{  
//Unchanged variables.
constexpr 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 PowerSpectrum =0; //pure number. Name given by my dear dsp Teacher Mr. Lyons.

//Sampling frequency and samples of segment.
int samplFreq = 50000; // sample/second.
int N = 1000; //sample.

// 1st existing sinusoidal.
double ampl_1 = 70000; //pure number.
double existFreq_1 = 36.7634; // Hz.
double phase_1 = 0.67 * pi; // rad.
double unitAngle_1 = (existFreq_1 / samplFreq) * (2 * pi); // rad/sample.

// 2nd existing sinusoidal.
double ampl_2 = 60000; // pure number.
double existFreq_2 = 4505.75; // Hz.
double phase_2 = -0.37 * pi; // rad.
double unitAngle_2 = (existFreq_2 / samplFreq) * (2 * pi); // rad/sample.

// Testing grid.
double testFreq = 0; // Hz.
double testUnitAngle = 0; // rad/sample.
double testAngle = 0; // rad.
double lowTestFreq = 35.2364; //Hz.
double highTestFreq = 40.7896; //Hz.
int M = 40; // pure number.
int m = 0; // pure number.
double testFreqStep = (highTestFreq - lowTestFreq) / M; // Hz.

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)
   + ampl_2 * sin(n * unitAngle_2 + phase_2);

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.
 PowerSpectrum = Re * Re + Im * Im; //pure number.       
 std::cout << " MagnSquared " << PowerSpectrum << std::endl;
}       
return 0;
}