/**
* Returns an array of complex numbers representing the frequency spectrum
* of real valued time domain sequence array. (count($array) must be integer power of 2)
* Inspired by http://rosettacode.org/wiki/Fast_Fourier_transform#Python
*
* @param array $array Real-valued series input, eg. time-series.
* @return array Array of complex numbers representing input signal in Fourier domain.
* @throws \Exception
*/
public static function fft($array)
{
$arrayLength = count($array);
if ($arrayLength <= 1) {
return array(new Complex($array[0], 0));
}
if (log($arrayLength) / M_LN2 % 1 !== 0) {
throw new \Exception('Array length must be integer power of 2');
}
$even = self::fft(self::segment($array, 0, 2));
$odd = self::fft(self::segment($array, 1, 2));
$result = array();
$halfLength = $arrayLength / 2;
for ($k = 0; $k < $arrayLength; ++$k) {
$phase = -2 * M_PI * $k / $arrayLength;
$phasor = new Complex(cos($phase), sin($phase));
if ($k < $halfLength) {
$result[$k] = $even[$k]->add($phasor->multiply($odd[$k]));
} else {
$result[$k] = $even[$k - $halfLength]->subtract($phasor->multiply($odd[$k - $halfLength]));
}
}
return $result;
}
/**
* Returns the cosine of this complex number.
*
* @return Complex the cosine of this complex number.
*/
public function cos()
{
$e = new Complex(M_E, 0);
$i = new Complex(0, 1);
$negativeI = new Complex(0, -1);
$numerator = $e->complexPow($i->multiply($this))->add($e->complexPow($negativeI->multiply($this)));
return $numerator->divide(new Complex(2, 0));
}