intwave (Wavelet Toolbox)

Integrate wavelet function psi.

[INTEG,XVAL] = intwave('wname',PREC)
[INTEG,XVAL] = intwave('wname',PREC,PFLAG)
[INTEG,XVAL] = intwave('wname')

Description

[INTEG,XVAL] = intwave('wname',PREC) returns values of the wavelet function

integrals INTEG (from

to XVAL values):

for x in XVAL.

The function

is approximated on the 2PREC points grid XVAL, where PREC is a positive integer. 'wname' is a string containing the name of the wavelet

(see wfilters).

When used with three arguments, the third one is a dummy argument.

[INTEG,XVAL] = intwave('wname',PREC,PFLAG) in addition plots INTEG on XVAL grid if PFLAG is nonzero.

[INTEG,XVAL] = intwave('wname',PREC) is equivalent to
[INTEG,XVAL] = intwave('wname',PREC,0).

[INTEG,XVAL] = intwave('wname') is equivalent to
[INTEG,XVAL] = intwave('wname',8).

intwave is used only for continuous analysis (see cwt).

Examples

% Set wavelet name. 
    wname = 'db4';

% Plot wavelet function. 
    [phi,psi,xval] = wavefun(wname,7);
    subplot(211); plot(xval,psi); title('Wavelet'); 

% Compute and plot wavelet integrals approximations 
% on a dyadic grid. 
    [integ,xval] = intwave(wname,7); 
    subplot(212); plot(xval,integ); 
    title(['Wavelet integrals over [-Inf x] ' ... 
        'for each value of xval']);

Algorithm

First, the wavelet function is approximated on a grid of 2^PREC points using wavefun. A piecewise constant interpolation is used in order to compute the integrals using cumsum.