Functions
static int	mpolar_grid (int T, int R, double x, double w)
	Generates the points $x_{t,j}$ with weights $w_{t,j}$ for the modified polar grid with angles and offsets.
static int	mpolar_dft (fftw_complex f_hat, int NN, fftw_complex f, int T, int R, int m)
	discrete mpolar FFT
static int	mpolar_fft (fftw_complex f_hat, int NN, fftw_complex f, int T, int R, int m)
	NFFT-based mpolar FFT.
static int	inverse_mpolar_fft (fftw_complex f, int T, int R, fftw_complex f_hat, int NN, int max_i, int m)
	inverse NFFT-based mpolar FFT
static int	comparison_fft (FILE *fp, int N, int T, int R)
	Comparison of the FFTW, mpolar FFT, and inverse mpolar FFT.
int	main (int argc, char **argv)
	test program for various parameters

Variables
double	GLOBAL_elapsed_time

Detailed Description

Function Documentation

static int mpolar_grid	(	int	T,
		int	R,
		double *	x,
		double *	w
	)

static

Generates the points $x_{t,j}$ with weights $w_{t,j}$ for the modified polar grid with $T$ angles and $R$ offsets.

We add more concentric circles to the polar grid and exclude those nodes not located in the unit square, i.e.,

$x_{t,j} := r_j\left(\cos\theta_t, \sin\theta_t\right)^{\top}\,,\qquad (j,t)^{\top}\in I_{\sqrt{2}R}\times I_T\,.$

with $r_j$ and $\theta_t$ as for the polar grid. The number of nodes for the modified polar grid can be estimated as $M \approx \frac{4}{\pi}\log(1+\sqrt{2}) T R$ .

Definition at line 63 of file mpolar_fft_test.c.

References PI.

Referenced by inverse_mpolar_fft(), main(), mpolar_dft(), and mpolar_fft().

Functions

Variables

Detailed Description

Function Documentation