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 isa
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 atscale1for
the points in . PL and PR are length(SigVal)-by-2
matrices. The left boundaries are(1-PL(:,2))./PL(:,1) and
therightboundariesare(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 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 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 isthe 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

Cone of influence for Mexican hat wavelet:

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

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

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:

andhas 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:

$$|t-u|\le sB$$

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