libftsh
A Fast Transform for Spherical Harmonics
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Contains the Matviyenko bells for local trigonometric transforms. More...
#include "libftsh.h"
Functions | |
REAL | bellcutoff (int laplength, int t) |
REAL | bellmat1 (int laplength, int t) |
REAL | bellmat2 (int laplength, int t) |
REAL | bellmat3 (int laplength, int t) |
REAL | bellmat4 (int laplength, int t) |
REAL | bellmat5 (int laplength, int t) |
REAL | bellmat6 (int laplength, int t) |
REAL | bellmat7 (int laplength, int t) |
REAL | bellmat8 (int laplength, int t) |
REAL | bellmat9 (int laplength, int t) |
REAL | bellmat10 (int laplength, int t) |
REAL | bellmat11 (int laplength, int t) |
REAL | bellmat12 (int laplength, int t) |
REAL | bellmat13 (int laplength, int t) |
REAL | bellmat14 (int laplength, int t) |
REAL | bellmat15 (int laplength, int t) |
REAL | bellmat16 (int laplength, int t) |
REAL | bellmat17 (int laplength, int t) |
REAL | bellmat18 (int laplength, int t) |
REAL | bellmat19 (int laplength, int t) |
REAL | bellmat20 (int laplength, int t) |
Contains the Matviyenko bells for local trigonometric transforms.
The bells have the form bell(laplength,t)
INPUTS:
OUTPUT: The bell function returns a REAL which is the bell's value at that point.
The bellmatXX sequence of bells is due to Gregory Matviyenko 'Optimized Local Trigonometric Bases' Research report YALEU/DCS/RR-1041 July 15, 1994 and Applied and Computational Harmonic Analysis 3 (1996)
The are not standard local cosine bells, but instead come in pairs, with one bell used for expansion and the other (dual) bell used for reconstruction.
These particular bells have been optimized after fixing a parameter N (?smoothness). Each N gives the best results for some cutoff epsilon_N. They are optimized in the sense that for a sin of arbitrary phase and frequency, they will, on average, yield the fewest coefficients above epsilon_N
(It's not clear from the paper whether s should begin at 0 or 1. formula (151) has a g_0 but table 1 starts with g_1. It should begin at 0.)
REAL bellcutoff | ( | int | laplength, |
int | t | ||
) |
bellcutoff is a characteristic function.
It is useful for tests when we want to quickly disable the effect of the bell