text: /* 
   * Free FFT and convolution (C++)
   * 
   * Copyright (c) 2017 Project Nayuki. (MIT License)
   * https://www.nayuki.io/page/free-small-fft-in-multiple-languages
   * 
   * Permission is hereby granted, free of charge, to any person obtaining a copy of
   * this software and associated documentation files (the "Software"), to deal in
   * the Software without restriction, including without limitation the rights to
   * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
   * the Software, and to permit persons to whom the Software is furnished to do so,
   * subject to the following conditions:
   * - The above copyright notice and this permission notice shall be included in
   *   all copies or substantial portions of the Software.
   * - The Software is provided "as is", without warranty of any kind, express or
   *   implied, including but not limited to the warranties of merchantability,
   *   fitness for a particular purpose and noninfringement. In no event shall the
   *   authors or copyright holders be liable for any claim, damages or other
   *   liability, whether in an action of contract, tort or otherwise, arising from,
   *   out of or in connection with the Software or the use or other dealings in the
   *   Software.
   */
  
  #pragma once
  
  #include <complex>
  #include <vector>
  
  
  namespace Fft {
  	
  	/* 
  	 * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
  	 * The vector can have any length. This is a wrapper function.
  	 */
  	void transform(std::vector<std::complex<double> > &vec);
  	
  	
  	/* 
  	 * Computes the inverse discrete Fourier transform (IDFT) of the given complex vector, storing the result back into the vector.
  	 * The vector can have any length. This is a wrapper function. This transform does not perform scaling, so the inverse is not a true inverse.
  	 */
  	void inverseTransform(std::vector<std::complex<double> > &vec);
  	
  	
  	/* 
  	 * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
  	 * The vector's length must be a power of 2. Uses the Cooley-Tukey decimation-in-time radix-2 algorithm.
  	 */
  	void transformRadix2(std::vector<std::complex<double> > &vec);
  	
  	
  	/* 
  	 * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
  	 * The vector can have any length. This requires the convolution function, which in turn requires the radix-2 FFT function.
  	 * Uses Bluestein's chirp z-transform algorithm.
  	 */
  	void transformBluestein(std::vector<std::complex<double> > &vec);
  	
  	
  	/* 
  	 * Computes the circular convolution of the given complex vectors. Each vector's length must be the same.
  	 */
  	void convolve(
  		const std::vector<std::complex<double> > &vecx,
  		const std::vector<std::complex<double> > &vecy,
  		std::vector<std::complex<double> > &vecout);
  	
  }
  