nfct_2d: 2-D NFCT/NFST

In gzt/rNFFT: Fast Fourier Transform at Nonequispaced Nodes

Description

The non-equispaced trigonometric transforms (sine and cosine) take non-uniform samples x from the $d$-dimensional torus [0,0.5)^d.

The NDCT functions compute the cosine transform directly. This is slow. The NFCT functions use the FFT to compute this, which should be faster. The adjoint, in this case, is not the same as the inverse. Solving the inverse problem requires approximations. Here we present the 2D NDCT, NFCT, and their adjoints. You most likely want to use the nfct_2d and nfct_adjoint_2d functions rather than the dct functions.

Usage

nfct_2d(x, f_hat)

ndct_2d(x, f_hat)

nfct_adjoint_2d(x, f, n0, n1)

ndct_adjoint_2d(x, f, n0, n1)

nfst_2d(x, f_hat)

ndst_2d(x, f_hat)

nfst_adjoint_2d(x, f, n0, n1)

ndst_adjoint_2d(x, f, n0, n1)

Arguments

x	two dimensional complex vector in [0,0.5)^2
f_hat	set of frequencies
f	frequencies for adjoint, same length as x
n0	number of frequencies in the first dimension for transform, specified for adjoint.
n1	number of frequencies in the second dimension for transform, specified for adjoint.

Details

2-D Non-equispaced Trigonometric Tranform

Functions

• ndct_2d:

• nfct_adjoint_2d:

• ndct_adjoint_2d:

• nfst_2d:

• ndst_2d:

• nfst_adjoint_2d:

• ndst_adjoint_2d:

Examples

set.seed(20190728)
x <- matrix(runif(2*32*14)*.5, ncol=2, byrow = TRUE)

f_hat = 1:(32*14)
for(i in 1:(32*14)) f_hat[i] = runif(1)
f_hatmatrix = matrix(f_hat, nrow = 32)
f_vector <- nfct_2d(x, f_hatmatrix)
fs_vector <-  nfst_2d(x, f_hatmatrix)
fd_vector <- ndct_2d(x, f_hatmatrix)
fsd_vector <-  ndst_2d(x, f_hatmatrix)
f_vector[1:3]
fd_vector[1:3]
fs_vector[1:3]
fsd_vector[1:3]
newf_hat <- nfct_adjoint_2d(x,f_vector,32,14)
newf_hat[1,1:7]
newdf_hat <- ndct_adjoint_2d(x,f_vector,32,14)
newdf_hat[1,1:7]
newfs_hat <- nfst_adjoint_2d(x,f_vector,32,14)
newfs_hat[1,1:7]
newdsf_hat <- ndst_adjoint_2d(x,f_vector,32,14)
newdsf_hat[1,1:7]

gzt/rNFFT documentation built on April 15, 2020, 6:07 p.m.