NFFT - Parameter

All parameters are stored in the plan. Using the simple initialisation nfft_init, one has only to define the multi bandwidth ${N}$ and the number of knots $M$. All other parameters are set to default values. The specific initialisation nfft_init_specific may be used to customise the library to one's needs.

Table 2: Parameters

name	default	description
${N}$		multivariate bandwidth
$M$		number of knots
${n}$	$2^{\left\lceil\log \mbox{\boldmath\scriptsize {${N}$}}\right\rceil}$	FFTW-size
$m$	see Table 3	cut off parameter in time domain
nfft_flags	PRE_PSI| PRE_PHI_HUT|	disjunction of flags for
	MALLOC_X| MALLOC_F_HAT| MALLOC_F|	memory allocation
	FFTW_INIT| FFT_OUT_OF_PLACE
fftw_flags	FFTW_ESTIMATE| FFTW_DESTROY_INPUT	disjunction of flags for FFTW

In Table 3 we give the default values for the cut off parameter $m$. This parameter depends on the window function and is choosen such that the error $E_{\infty }$ (see Section 4) is smaller than $10^{-12}$.

Table: Default values for the cut-off parameter $m$, see also Section 4,Figure 3.

window function	Kaiser-Bessel	${\rm sinc}^{2m}$	$B$-spline	Gaussian
$m$	6	9	11	12