我正在尝试使用 Accelerate vDSP 框架将现有的基于 FFT 的低通滤波器移植到 iOS。
FFT 似乎在样本的前 1/4 中按预期工作。但在那之后结果似乎是错误的，甚至更奇怪的是镜像（信号的后半部分反映了前半部分的大部分）。
您可以从下面的测试应用程序中看到结果。首先绘制原始采样数据，然后是预期过滤结果的示例（过滤掉高于 15Hz 的信号），最后是我当前 FFT 代码的结果（请注意，预期结果和示例 FFT 结果的比例不同于原始数据）：
我的低通滤波器的实际代码如下：
double *lowpassFilterVector(double *accell, uint32_t sampleCount, double lowPassFreq, double sampleRate )
{
double stride = 1;
int ln = log2f(sampleCount);
int n = 1 << ln;
// So that we get an FFT of the whole data set, we pad out the array to the next highest power of 2.
int fullPadN = n * 2;
double *padAccell = malloc(sizeof(double) * fullPadN);
memset(padAccell, 0, sizeof(double) * fullPadN);
memcpy(padAccell, accell, sizeof(double) * sampleCount);
ln = log2f(fullPadN);
n = 1 << ln;
int nOver2 = n/2;
DSPDoubleSplitComplex A;
A.realp = (double *)malloc(sizeof(double) * nOver2);
A.imagp = (double *)malloc(sizeof(double) * nOver2);
// This can be reused, just including it here for simplicity.
FFTSetupD setupReal = vDSP_create_fftsetupD(ln, FFT_RADIX2);
vDSP_ctozD((DSPDoubleComplex*)padAccell,2,&A,1,nOver2);
// Use the FFT to get frequency counts
vDSP_fft_zripD(setupReal, &A, stride, ln, FFT_FORWARD);
const double factor = 0.5f;
vDSP_vsmulD(A.realp, 1, &factor, A.realp, 1, nOver2);
vDSP_vsmulD(A.imagp, 1, &factor, A.imagp, 1, nOver2);
A.realp[nOver2] = A.imagp[0];
A.imagp[0] = 0.0f;
A.imagp[nOver2] = 0.0f;
// Set frequencies above target to 0.
// This tells us which bin the frequencies over the minimum desired correspond to
NSInteger binLocation = (lowPassFreq * n) / sampleRate;
// We add 2 because bin 0 holds special FFT meta data, so bins really start at "1" - and we want to filter out anything OVER the target frequency
for ( NSInteger i = binLocation+2; i < nOver2; i++ )
{
A.realp[i] = 0;
}
// Clear out all imaginary parts
bzero(A.imagp, (nOver2) * sizeof(double));
//A.imagp[0] = A.realp[nOver2];
// Now shift back all of the values
vDSP_fft_zripD(setupReal, &A, stride, ln, FFT_INVERSE);
double *filteredAccell = (double *)malloc(sizeof(double) * fullPadN);
// Converts complex vector back into 2D array
vDSP_ztocD(&A, stride, (DSPDoubleComplex*)filteredAccell, 2, nOver2);
// Have to scale results to account for Apple's FFT library algorithm, see:
// http://developer.apple.com/library/ios/#documentation/Performance/Conceptual/vDSP_Programming_Guide/UsingFourierTransforms/UsingFourierTransforms.html#//apple_ref/doc/uid/TP40005147-CH202-15952
double scale = (float)1.0f / fullPadN;//(2.0f * (float)n);
vDSP_vsmulD(filteredAccell, 1, &scale, filteredAccell, 1, fullPadN);
// Tracks results of conversion
printf("\nInput & output:\n");
for (int k = 0; k < sampleCount; k++)
{
printf("%3d\t%6.2f\t%6.2f\t%6.2f\n", k, accell[k], padAccell[k], filteredAccell[k]);
}
// Acceleration data will be replaced in-place.
return filteredAccell;
}
在原始代码中，该库处理非二次幂大小的输入数据；在我的 Accelerate 代码中，我将输入填充到最接近的 2 次幂。在原始样本数据下方的样本测试的情况下，原始样本数据是 1000 个样本，因此它被填充到 1024。我认为这不会影响结果，但为了可能的差异，我将其包括在内。
如果您想尝试解决方案，可以在此处下载生成图表的示例项目（在 FFTTest 文件夹中）：
感谢您提供任何见解，我以前没有使用过 FFT，所以我觉得我错过了一些关键的东西。