conofinf

Cone of influence

Syntax

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

Description

cone = conofinf(wname,scales,LenSig,SigVal) returns the cone of influence (COI) for the wavelet wname at the scales in scales and positions in SigVal. LenSig is the length of the input signal. If SigVal is a scalar, cone is a matrix with row dimension length(scales) and column dimension LenSig. If SigVal is a vector, cone is cell array of matrices.

[cone,PL,PR] = conofinf(wname,scales,LenSig,SigVal) returns the left and right boundaries of the cone of influence at scale 1 for the points in SigVal. PL and PR are length(SigVal)-by-2 matrices. The left boundaries are(1-PL(:,2))./PL(:,1) and the right boundaries are(1-PR(:,2))./PR(:,1).

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

[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 character vector or string scalar 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 and must exceed the maximum of `SigVal`.
`SigVal`	`SigVal` is a vector of signal values at which to compute the cone of influence. The largest value of `SigVal` must be less than the signal length, `LenSig`.If `SigVal` is empty, `conofinf` returns the slope and intercept terms for the minimal left and maximal right vertices of the cone of influence.

Output Arguments

`cone`	`cone` is the cone of influence. If `SigVal` is a scalar, `cone` is a matrix. The row dimension is equal to the number of `scales` and column dimension equal to the signal length, `LenSig`. If `SigVal` 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 `SigVal` corresponding to the cone of influence.
`PL`	`PL` is the minimum value of the cone of influence on the position (time) axis.
`PR`	`PR` is the maximum value of the cone of influence on the position (time) axis.
`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)` is the slope and `PLmin(2)` is the point where the line intercepts the scale axis.
`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)` is the slope and `PRmax(2)` is the point where the line intercepts the scale axis.

Examples

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Cone of Influence for Mexican Hat or Ricker Wavelet

Open Live Script

Load the data.

load cuspamax
signal = cuspamax;

Set up the wavelet.

wname  = 'mexh';
scales = 1:64;
lenSIG = length(signal);
x = 500;

Plot the wavelet.

figure;
cwt(signal,scales,wname,'plot');

Plot the cone of influence.

hold on
[cone,PL,PR,Pmin,Pmax] = conofinf(wname,scales,lenSIG,x,'plot');
set(gca,'Xlim',[1 lenSIG])

Cone of Influence Minimal and Maximal Vertices

Open Live Script

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

[PLmin,PRmax] = conofinf('morl',1:32,1024,[],'plot');

PLmin

PLmin = 1×2

   -0.1245   32.0000

PRmax

PRmax = 1×2

    0.1250  -96.0000

More About

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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, the dilated and translated wavelet is:

$ψ_{u, s} (t) = \frac{1}{\sqrt{s}} ψ (\frac{t - u}{s})$

and 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 is equivalent to:

$| t - u | \leq s B$

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

References

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

Documentation