%WAVE_BASES  1D Wavelet functions Morlet, Paul, or DOG%%  [DAUGHTER,FOURIER_FACTOR,COI,DOFMIN] = ...%      wave_bases(MOTHER,K,SCALE,PARAM);%%   Computes the wavelet function as a function of Fourier frequency,%   used for the wavelet transform in Fourier space.%   (This program is called automatically by WAVELET)%% INPUTS:%%    MOTHER = a string, equal to 'MORLET' or 'PAUL' or 'DOG'%    K = a vector, the Fourier frequencies at which to calculate the wavelet%    SCALE = a number, the wavelet scale%    PARAM = the nondimensional parameter for the wavelet function%% OUTPUTS:%%    DAUGHTER = a vector, the wavelet function%    FOURIER_FACTOR = the ratio of Fourier period to scale%    COI = a number, the cone-of-influence size at the scale%    DOFMIN = a number, degrees of freedom for each point in the wavelet power%             (either 2 for Morlet and Paul, or 1 for the DOG)%%----------------------------------------------------------------------------%   Copyright (C) 1995-1998, Christopher Torrence and Gilbert P. Compo%   University of Colorado, Program in Atmospheric and Oceanic Sciences.%   This software may be used, copied, or redistributed as long as it is not%   sold and this copyright notice is reproduced on each copy made.  This%   routine is provided as is without any express or implied warranties%   whatsoever.%----------------------------------------------------------------------------function [daughter,fourier_factor,coi,dofmin] = ...	wave_bases(mother,k,scale,param);mother = upper(mother);n = length(k);if (strcmp(mother,'MORLET'))  %-----------------------------------  Morlet	if (param == -1), param = 6.;, end	k0 = param;	expnt = -(scale.*k - k0).^2/2.*(k > 0.);	norm = sqrt(scale*k(2))*(pi^(-0.25))*sqrt(n);    % total energy=N   [Eqn(7)]	daughter = norm*exp(expnt);	daughter = daughter.*(k > 0.);     % Heaviside step function	fourier_factor = (4*pi)/(k0 + sqrt(2 + k0^2)); % Scale-->Fourier [Sec.3h]	coi = fourier_factor/sqrt(2);                  % Cone-of-influence [Sec.3g]	dofmin = 2;                                    % Degrees of freedomelseif (strcmp(mother,'PAUL'))  %--------------------------------  Paul	if (param == -1), param = 4.;, end	m = param;	expnt = -(scale.*k).*(k > 0.);	norm = sqrt(scale*k(2))*(2^m/sqrt(m*prod(2:(2*m-1))))*sqrt(n);	daughter = norm*((scale.*k).^m).*exp(expnt);	daughter = daughter.*(k > 0.);     % Heaviside step function	fourier_factor = 4*pi/(2*m+1);	coi = fourier_factor*sqrt(2);	dofmin = 2;elseif (strcmp(mother,'DOG'))  %--------------------------------  DOG	if (param == -1), param = 2.;, end	m = param;	expnt = -(scale.*k).^2 ./ 2.0;	norm = sqrt(scale*k(2)/gamma(m+0.5))*sqrt(n);	daughter = -norm*(i^m)*((scale.*k).^m).*exp(expnt);	fourier_factor = 2*pi*sqrt(2./(2*m+1));	coi = fourier_factor/sqrt(2);	dofmin = 1;else	error('Mother must be one of MORLET,PAUL,DOG')endreturn% end of code