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# 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 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 or Ricker 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):

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

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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:

`${\psi }_{u,s}\left(t\right)=\frac{1}{\sqrt{s}}\psi \left(\frac{t-u}{s}\right)$`

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.

## References

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