NFFT: NNFFT - Nonequispaced in time and frequency FFT

NFFT 3.4.1

Direct and fast computation of the discrete nonequispaced in time and frequency Fourier transform. More...

Data Structures
struct	nnfft_plan
	data structure for an NNFFT (nonequispaced in time and frequency fast Fourier transform) plan with double precision More...

Macros
#define	MALLOC_V (1U<< 11)

Functions
void	nnfft_init (nnfft_plan ths_plan, int d, int N_total, int M_total, int N)

void	nnfft_init_guru (nnfft_plan ths_plan, int d, int N_total, int M_total, int N, int *N1, int m, unsigned nnfft_flags)

void	nnfft_trafo (nnfft_plan *ths_plan)
	user routines More...

void	nnfft_adjoint (nnfft_plan *ths_plan)

void	nnfft_precompute_lin_psi (nnfft_plan *ths_plan)
	create a lookup table More...

void	nnfft_precompute_psi (nnfft_plan *ths_plan)

void	nnfft_precompute_full_psi (nnfft_plan *ths_plan)
	computes all entries of B explicitly More...

void	nnfft_precompute_phi_hut (nnfft_plan *ths_plan)
	initialisation of direct transform More...

void	nnfft_finalize (nnfft_plan *ths_plan)

Detailed Description

Direct and fast computation of the discrete nonequispaced in time and frequency Fourier transform.

Macro Definition Documentation

#define MALLOC_V (1U<< 11)

If this flag is set, (de)allocation of the frequency node vector is done.

See Also: nnfft_init; nnfft_init_guru; nnfft_finalize

Author: Tobias Knopp

Definition at line 425 of file nfft3.h.

Referenced by nnfft_finalize(), nnfft_init(), and reconstruct().

Function Documentation

nnfft_init	(	nnfft_plan *	ths_plan,
		int	d,
		int	N_total,
		int	M_total,
		int *	N
	)

Creates a transform plan.

ths_plan The plan for the transform
d The dimension
N_total The number of nodes
M_total The number of nodes
N The bandwidth

Author: Tobias Knopp

Definition at line 612 of file nnfft.c.

References nnfft_plan::d, FFT_OUT_OF_PLACE, FFTW_INIT, nnfft_plan::m, nnfft_plan::M_total, MALLOC_F, MALLOC_F_HAT, MALLOC_V, MALLOC_X, nnfft_plan::N, nnfft_plan::N1, nnfft_plan::N_total, nfft_malloc(), nnfft_plan::nnfft_flags, PRE_PHI_HUT, and PRE_PSI.

void nnfft_init_guru	(	nnfft_plan *	ths_plan,
		int	d,
		int	N_total,
		int	M_total,
		int *	N,
		int *	N1,
		int	m,
		unsigned	nnfft_flags
	)

Creates a transform plan.

ths_plan The plan for the transform
d The dimension
N_total The number of nodes
M_total The number of nodes
N The bandwidth
N1 The oversampled bandwidth
m The cut-off parameter
nnfft_flags The flags

Author: Tobias Knopp

Definition at line 577 of file nnfft.c.

References nnfft_plan::d, FFT_OUT_OF_PLACE, FFTW_INIT, nnfft_plan::m, nnfft_plan::M_total, MALLOC_F_HAT, nnfft_plan::N, nnfft_plan::N1, nnfft_plan::N_total, nfft_malloc(), nnfft_plan::nnfft_flags, PRE_FULL_PSI, PRE_LIN_PSI, PRE_PHI_HUT, and PRE_PSI.

Referenced by reconstruct().

void nnfft_trafo ( nnfft_plan * ths_plan )

user routines

Executes a NNFFT, i.e. computes for $j=0,...,M_{total}-1$

$f(x_j) = \sum_{k = 0}^{N_{total}-1} \hat{f}(v_k) {\rm e}^{-2 \pi \mbox{\rm\scriptsize i} v_k x_j \odot N}$

ths_plan The plan

Author: Tobias Knopp

Definition at line 291 of file nnfft.c.

References nnfft_plan::d, nnfft_plan::direct_plan, nfft_plan::f, nnfft_plan::f, nnfft_plan::M_total, nfft_trafo(), nnfft_plan::sigma, and nnfft_plan::x.

void nnfft_adjoint ( nnfft_plan * ths_plan )

Executes a adjoint NNFFT, i.e. computes for $k=0,...,N_{total}-1$

$\hat{f}(v_k) = \sum_{j = 0}^{M_{tota}l-1} f(x_j) {\rm e}^{2 \pi \mbox{\rm\scriptsize i} v_k x_j \odot N}$

ths_plan The plan

Author: Tobias Knopp

Definition at line 319 of file nnfft.c.

References nnfft_plan::d, nnfft_plan::direct_plan, nfft_plan::f, nnfft_plan::f, nnfft_plan::M_total, nfft_adjoint(), nnfft_plan::sigma, and nnfft_plan::x.

void nnfft_precompute_lin_psi ( nnfft_plan * ths_plan )

create a lookup table

Precomputation for a transform plan.

ths_plan The pointer to a nfft plan

Author: Tobias Knopp

precomputes equally spaced values of the window function psi

if PRE_LIN_PSI is set the application program has to call this routine

Definition at line 367 of file nnfft.c.

References nnfft_plan::d, nnfft_plan::direct_plan, nnfft_plan::K, nnfft_plan::m, nnfft_plan::n, nnfft_plan::N1, nfft_precompute_lin_psi(), and nnfft_plan::psi.

Referenced by reconstruct().

void nnfft_precompute_psi ( nnfft_plan * ths_plan )

Precomputation for a transform plan.

ths_plan The pointer to a nfft plan

Author: Tobias Knopp

precomputes the values of the window function psi in a tensor product form

if PRE_PSI is set the application program has to call this routine after setting the nodes x

Definition at line 385 of file nnfft.c.

References nnfft_plan::d, nnfft_plan::direct_plan, nnfft_plan::m, nnfft_plan::M_total, nnfft_plan::n, nnfft_plan::N1, nnfft_plan::N_total, nfft_precompute_psi(), nnfft_plan::psi, nnfft_plan::sigma, nnfft_plan::v, and nnfft_plan::x.

Referenced by nnfft_precompute_full_psi(), and reconstruct().

void nnfft_precompute_full_psi ( nnfft_plan * ths_plan )

computes all entries of B explicitly

Precomputation for a transform plan.

ths_plan The pointer to a nfft plan

Author: Tobias Knopp

precomputes the values of the window function psi and their indices in non tensor product form

if PRE_FULL_PSI is set the application program has to call this routine after setting the nodes x

Definition at line 424 of file nnfft.c.

References nnfft_plan::d, nnfft_plan::direct_plan, nnfft_plan::m, nnfft_plan::M_total, nfft_precompute_full_psi(), nnfft_precompute_psi(), nnfft_plan::psi, nnfft_plan::psi_index_f, nnfft_plan::psi_index_g, nnfft_plan::sigma, and nnfft_plan::x.

Referenced by reconstruct().

void nnfft_precompute_phi_hut ( nnfft_plan * ths_plan )

initialisation of direct transform

Precomputation for a transform plan.

ths_plan The pointer to a nfft plan

Author: Tobias Knopp

precomputes the values of the fourier transformed window function, i.e. phi_hut

if PRE_PHI_HUT is set the application program has to call this routine after setting the nodes v

Definition at line 347 of file nnfft.c.

References nnfft_plan::c_phi_inv, nnfft_plan::d, nnfft_plan::M_total, nnfft_plan::n, nnfft_plan::N, nfft_malloc(), and nnfft_plan::x.

Referenced by reconstruct().

void nnfft_finalize ( nnfft_plan * ths_plan )

Destroys a plan.

ths_plan The plan

Author: Tobias Knopp

Definition at line 655 of file nnfft.c.

References nnfft_plan::aN1, nnfft_plan::c_phi_inv, nnfft_plan::direct_plan, nnfft_plan::f, nnfft_plan::f_hat, MALLOC_F, MALLOC_F_HAT, MALLOC_V, MALLOC_X, nnfft_plan::N, nnfft_plan::N1, nfft_finalize(), nfft_free(), nnfft_plan::nnfft_flags, PRE_FULL_PSI, PRE_LIN_PSI, PRE_PHI_HUT, PRE_PSI, nnfft_plan::psi, nnfft_plan::psi_index_f, nnfft_plan::psi_index_g, nnfft_plan::v, and nnfft_plan::x.

Referenced by reconstruct().