typedef struct Complex Complex;
typedef struct Freq Freq;
struct Complex
{
	double r, i;
};

struct Freq
{
	double f, r, a;
};

void C_to_F(Complex *c, Freq *f);
void ri_to_F(double r, double i, Freq *f);
void ris_to_fs(int n, double rex[], double imx[], Freq f[]);
void fft_bit_reversal(int n, double rex[], double imx[]);
void fft_butterfly(int n, double rex[], double imx[]);
void fft(int n, double rex[], double imx[]);
void ifft(int n, double rex[], double imx[]);
void dft(int n, double rex[], double imx[]);
void idftx(int n, double rex[], double imx[], Complex *cx, double a);
void idft(int n, double rex[], double imx[]);
void separate_odd_even(int n, double rex[], double imx[]);
void odd_even_freq_decomp(int n, double rex[], double imx[]);
void fftr(int n, double rex[], double imx[]);
void ifftr(int n, double rex[], double imx[]);