matbells.c File Reference

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)

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Detailed Description

Contains the Matviyenko bells for local trigonometric transforms.

The bells have the form bell(laplength,t)

INPUTS:

• laplength-- the number of POINTS the bell spills out of the interval. It also spills in an equal number of points. Thus the bell takes 2*laplength points to rise from 0 to 1.
• t -- Which point you want to evaluate the bell at. This should range from 0 to 2*laplength-1. bell(laplength,0)=~0 then it rises until bell(laplength,2*laplength-1)=~1. The edge of the interval is between points, at t=(laplength-1) +0.5

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.)

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Function Documentation

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