// -*- C++ -*-
// automatically generated by autodoc

// ========== HEADER FILE src/chirpzt/chirpzt.h: ==========

// chirp z-transform
// ----- SRCFILE=src/chirpzt/fftarblen.cc: -----
static inline void make_fft_chirp(Complex *w, ulong n, ulong nn, int is);
// For k=0..n-1:   w[k] := exp( is * k*k * (i*2*PI/n)/2 )  where i = sqrt(-1)
// For k=n..nn-1:  w[k] = 0

void fft_arblen(Complex *x, ulong n, int is);
// Arbitrary length FFT.

// ----- SRCFILE=src/chirpzt/fftfract.cc: -----
static inline void make_fft_fract_chirp(Complex *w, double v, ulong n, ulong nn);
// For k=0..nn-1:   w[k] == exp(v*sqrt(-1)*k*k*2*pi*/n/2)

void fft_fract(Complex *x, ulong n, double v);
// Fractional (fast) Fourier transform.
// For complex array c[0...n]
// compute \sum_{x=0}^{n}{c_x*exp(is*v*2*i*\pi*x*k/n)}
//  (for v==1.0 this is just the usual fft)
// Use n*k == n^2/2 + k^2/2 - (k-n)^2/2
// See: Nussbaumer: "Fast Fourier Transform and Convolution Algorithms", chap.5, p.113ff
// Could use n*k == - n^2/2 - k^2/2 + (k+n)^2/2 instead.
// Worst case if n=2^x+1:
//   then nn=2*2^x
//   work is about 6 times of an FFT of length 2^x
//   and allocated workspace =2*nn

static inline void make_fft_fract_chirp(double *wr, double *wi, double v, ulong n, ulong nn);
// For k=0..nn-1:   Complex(wr[k],wi[k]) == exp(v*sqrt(-1)*k*k*2*pi*/n/2)

void fft_fract(double *x, double *y, ulong n, double v);
// Fractional (fast) fourier transform.
// For complex array c[0...n]
// compute \sum_{x=0}^{n}{c_x*exp(is*v*2*i*\pi*x*k/n)}
//  (for v==1.0 this is just the usual fft)
// Use n*k == n^2/2 + k^2/2 - (k-n)^2/2
// See: Nussbaumer: "Fast Fourier Transform and Convolution Algorithms", chap.5, p.113ff
// Could use n*k == - n^2/2 - k^2/2 + (k+n)^2/2 instead.
// Worst case if n=2^x+1:
//   then nn=4*2^x
//   work is about 12 times of an FFT of length 2^x
//   and allocated workspace =4*nn

// ----- SRCFILE=src/chirpzt/slowfracft.cc: -----
void slow_fract_ft(double *fr, double *fi, ulong n, double v);
// (slow) fractional Fourier transform.
// (for v=+-1 this is the usual Fourier transform)

void slow_fract_ft(Complex *f, ulong n, double v);
// (slow) fractional Fourier transform.
// (for v=+-1 this is the usual Fourier transform)

// ----- SRCFILE=src/chirpzt/slowzt.cc: -----
void slow_zt(Complex *f, ulong n, Complex z);
// (slow) z-transform.

void slow_zt(double *f, ulong n, double z);
// (slow) z-transform.

