public static DecomposedSongSegment DFT(this Song song)
{
//only frequences up to half of the sampling rate can be represented
int maxFreq = song.Sound.Length / 2;
DecomposedSongSegment output = new DecomposedSongSegment(maxFreq)
{
SamplingRate = song.SamplingRate
};
//for every frequency we can calculate
for (int freq = 0; freq < maxFreq; freq += 1)
{
//if not integer index, skip
decimal index = freq == 0 ? 0 : freq / ((decimal)song.Sound.Length / song.Data.SampleRate);
if ((index % 1) != 0)
{
continue;
}
Complex tempOutput = new Complex();
//calculate the raw output at a given frequency using the standard formula for discrete fourier transform
for (int sample = 0; sample < song.Sound.Length; sample++)
{
double angle = -2d * Math.PI * freq * sample / song.Sound.Length;
tempOutput += song.Sound[sample] * new Complex(angle);
}
//convert raw output to useful value
output.Audio[(int)index] = Math.Round(2 * tempOutput.Magnitude / song.Sound.Length, 5);
}
return(output);
}
public void DFTTest(string path, double[] output)
{
Song song = Wav.Read(path);
DecomposedSongSegment dss = song.DFT();
foreach (var(amplitude, index) in dss.Audio.Select((x, i) => (x, i)))
{
if (index > output.Length - 1)
{
Assert.AreEqual(0, amplitude, 5e-4);
}
else
{
Assert.AreEqual(output[index], amplitude, 5e-4);
}
}
}
