Use FFT for calculating AKF

PitchTracker/FFT/FFT.h

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+/**********************************************************************
+
+  FFT.h
+
+  Dominic Mazzoni
+
+  September 2000
+
+  This file contains a few FFT routines, including a real-FFT
+  routine that is almost twice as fast as a normal complex FFT,
+  and a power spectrum routine which is more convenient when
+  you know you don't care about phase information.  It now also
+  contains a few basic windowing functions.
+
+  Some of this code was based on a free implementation of an FFT
+  by Don Cross, available on the web at:
+
+    http://www.intersrv.com/~dcross/fft.html
+
+  The basic algorithm for his code was based on Numerical Recipes
+  in Fortran.  I optimized his code further by reducing array
+  accesses, caching the bit reversal table, and eliminating
+  float-to-double conversions, and I added the routines to
+  calculate a real FFT and a real power spectrum.
+
+  Note: all of these routines use single-precision floats.
+  I have found that in practice, floats work well until you
+  get above 8192 samples.  If you need to do a larger FFT,
+  you need to use doubles.
+
+**********************************************************************/
+
+/*
+ * This is the function you will use the most often.
+ * Given an array of floats, this will compute the power
+ * spectrum by doing a Real FFT and then computing the
+ * sum of the squares of the real and imaginary parts.
+ * Note that the output array is half the length of the
+ * input array, and that NumSamples must be a power of two.
+ */
+
+void PowerSpectrum(int NumSamples, float *In, float *Out);
+
+/*
+ * Computes an FFT when the input data is real but you still
+ * want complex data as output.  The output arrays are the
+ * same length as the input, but will be conjugate-symmetric
+ * NumSamples must be a power of two.
+ */
+
+void RealFFT(int NumSamples,
+             float *RealIn, float *RealOut, float *ImagOut);
+
+/*
+ * Computes an Inverse FFT when the input data is conjugate symmetric
+ * so the output is purely real.  NumSamples must be a power of
+ * two.
+ * Requires: EXPERIMENTAL_USE_REALFFTF
+ */
+void InverseRealFFT(int NumSamples,
+					float *RealIn, float *ImagIn, float *RealOut);
+
+void RealInverseRealFFT(int NumSamples,	float *In, float *Out);
+
+void DeinitFFT();