conofinf - Cone of influence

Syntax

cone = conofinf(wname,scales,LenSig,COIval) [cone,PL,PR] = conofinf(wname,scales,LenSig,COIval) [cone,PL,PR,PLmin,PRmax] = conofinf(wname,scales,LenSig,COIval) [PLmin,PRmax] = conofinf(wname,scales,LenSig) [...] = conofinf(...,'plot')

Description

cone = conofinf(wname,scales,LenSig,COIval) returns the cone of influence (COI) for the wavelet wname at the scales in scales and positions in COIval. LenSig represents the length of the input signal. If COIval is a scalar, cone is a matrix with row dimension length(scales) and column dimension LenSig. If COIval is a vector, cone is a cell array of matrices. COIval can be a value outside of the interval [1, LenSig].

[cone,PL,PR] = conofinf(wname,scales,LenSig,COIval) returns the equations of the left and right boundaries of the cone of influence for the points in COIval. PL and PR are length(COIval)-by-2 matrices. The first column contains the slope and the second column contains the scale-axis intercept of the lines defining the left and right COI boundaries. The left and right boundaries of the COI at a given scale, Scal, are(Scal-PL(:,2))./PL(:,1) and (Scal-PR(:,2))./PR(:,1).

[cone,PL,PR,PLmin,PRmax] = conofinf(wname,scales,LenSig,COIval) returns the equations of the lines that define the minimal left and maximal right boundaries of the cone of influence. PLmin and PRmax are 1-by-2 row vectors where PLmin(1) and PRmax(1) are the slopes of the lines. PLmin(2) and PRmax(2) are the points where the lines intercept the scale axis at the maximum scale value in scales.

[PLmin,PRmax] = conofinf(wname,scales,LenSig) returns the slope and intercept terms for the first-degree polynomials defining the minimal left and maximal right vertices of the cone of influence.

[...] = conofinf(...,'plot') plots the cone of influence.

Input Arguments

`wname`	`wname` is a string corresponding to a valid wavelet. To verify that `wname` is a valid wavelet, `wavemngr('fields',wname)` must return a struct array with a `type` field of 1 or 2, or a nonempty `bound` field.
`scales`	`scales` is a vector of scales over which to compute the cone of influence. Larger scales correspond to stretched versions of the wavelet and larger boundary values for the cone of influence.
`LenSig`	`LenSig` is the signal length.
`COIval`	`COIval` is a vector of values at which to compute the cone of influence. If `COIval` is empty, `conofinf` returns the slope and intercept terms for the minimal left and maximal right vertices of the cone of influence. `COIval` can be a value outside of the interval [1, `LenSig`].

Output Arguments

`cone`	`cone` is the cone of influence. If `COIval` is a scalar value, `cone` is a matrix. The row dimension equals the number of `scales` and the column dimension equals the signal length, `LenSig`. If `COIval` is a vector, `cone` is a cell array of matrices. The elements of each row of the matrix are equal to 1 in the interval around `COIval` corresponding to the cone of influence.
`PL`	`PL` contains the slope and intercept terms of the left (minimal) edge of the cone of influence. If `COIval` is a scalar, `PL` is a 1-by-2 row vector. If `COIval` is a vector, `PL` is a two-column matrix with row dimension equal to the length of `COIval`.
`PR`	`PR` contains the slope and intercept terms of the right (maximal) edge of the cone of influence. If `COIval` is a scalar, `PR` is a 1-by-2 row vector. If `COIval` is a vector, `PR` is a two-column matrix with row dimension equal to the length of `COIval`.
`PLmin`	`PLmin` is a 1-by-2 row vector containing the slope and scale axis intercept of the line defining the minimal left vertex of the cone of influence. `PLmin(1)` indicates the slope and `PLmin(2)` indicates the point where the line intercepts the scale axis at the maximum scale value.
`PRmax`	`PRmax` is a 1-by-2 row vector containing the slope and scale axis intercept of the line defining the maximal right vertex of the cone of influence. `PRmax(1)` indicates the slope and `PRmax(2)` indicates the point where the line intercepts the scale axis at the maximum scale value.

Definitions

Cone of Influence

Let ψ(t) be an admissible wavelet. Assume that the effective support of ψ(t) is [-B,B]. Letting u denote the translation parameter and s denote the scale parameter, you obtain the dilated and translated wavelet as follows:

The translated and dilated wavelet has effective support [u-sB,u+sB]. The cone of influence (COI) is the set of all t included in the effective support of the wavelet at a given position and scale. This set equals

At each scale, the COI determines the set of wavelet coefficients influenced by the value of the signal at a specified position.

Examples

Cone of influence for Mexican hat wavelet.

load cuspamax
signal = cuspamax;
wname  = 'mexh';
scales = 1:64;
lenSIG = length(signal);
COIval = 500;
figure;
cwt(signal,scales,wname,'plot');
hold on
[cone,PL,PR,Pmin,Pmax] = conofinf(wname,scales,lenSIG,COIval,'plot');

Left minimal and right maximal vertices for the cone of influence (Morlet wavelet).

[PLmin,PRmax] = conofinf('morl',1:32,1024,[],'plot');
% PLmin = -0.1245*u+ 32.0000  
% PRmax =  0.1250*u-96.0000

References

Mallat, S. A Wavelet Tour of Signal Processing, London: Academic Press, 1999, p. 174.

Tutorials

How To

1-D Continuous Wavelet Analysis

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