如何有效地确定用于循环的预渲染正弦波音频缓冲器的最小必要大小？

Question

我目前解决这个问题的方法是强力：我尝试所有可能的循环计数，看看其中是否有任何循环计数导致缓冲区大小包含整数个样本。我认为这种做法不能令人满意，原因如下：

1）效率很低。例如，下图所示的程序（在0Hz到48kHz之间打印480,000个可能频率值的缓冲区大小结果）在我2.7GHz的机器上需要35分钟才能完成。我想一定有更快的方法来完成这件事。

2）我怀疑结果不是100%准确，因为浮点错误。

提前感谢您的任何建议！

#include <stdio.h>
#include <math.h>

static const long long SAMPLES_PER_SECOND              = 96000;
static const long long MAX_ALLOWED_BUFFER_SIZE_SAMPLES = (SAMPLES_PER_SECOND * 10);

// Returns the length of the pre-render buffer needed to properly
// loop a sine wave at the given frequence, or -1 on failure.
static int GetNumCyclesNeededForPreRenderedBuffer(float freqHz)
{
   double oneCycleLengthSamples = SAMPLES_PER_SECOND/freqHz;

   for (int count=1; (count*oneCycleLengthSamples) < MAX_ALLOWED_BUFFER_SIZE_SAMPLES; count++)
   {
      double remainder = fmod(oneCycleLengthSamples*count, 1.0);
      if (remainder > 0.5) remainder = 1.0-remainder;
      if (remainder <= 0.0) return count;
   }
   return -1;
}

int main(int, char **)
{
   for (int i=0; i<48000*10; i++)
   {
      double freqHz = ((double)i)/10.0f;
      int numCyclesNeeded = GetNumCyclesNeededForPreRenderedBuffer(freqHz);
      if (numCyclesNeeded >= 0)
      {
         double oneCycleLengthSamples = SAMPLES_PER_SECOND/freqHz;
         printf("For %.1fHz, use a pre-render-buffer size of %f samples (%i cycles, %f samples/cycle)\n", freqHz, (numCyclesNeeded*oneCycleLengthSamples), numCyclesNeeded, oneCycleLengthSamples);
      }
      else printf("For %.1fHz, there was no suitable pre-render-buffer size under the allowed limit!\n", freqHz);
   }
   return 0;
}

Answer 1

number_of_cycles/size_of_buffer = frequency/samples_per_second