7.3.m

产生高斯脉冲的前15阶导函数。该函数的输入参数为：矢量t定义时间轴；高斯脉冲导函数的阶数k

%
% FUNCTION 7.3:"cp0702_analytical_waveforms"
%
% Definition of the analytical expression for the first 15
% derivatives of the Gaussian pulse
%
% The function receives as input:
% 1) the time axis vector 't'
% 2) the order of the derivative 'k'
% 3) the value of the shape factor 'alpha'
%
% The function returns the vector representing the
% derivative of order 'k' of the Gaussian pulse calculated
% over the time axis 't'
%
% Programmed by Luca De Nardis

function [deriv]=cp0702_analytical_waveforms(t,k,alpha)
switch(k)
    case 1
        deriv=4*pi*t/alpha^2.*exp(-2*pi*t.^2/alpha^2);
    case 2
        deriv=-4*pi*exp(-2*pi*(t.^2)/alpha^2).*...
            (-alpha^2+4*pi*(t.^2))/alpha^4;
    case 3
        deriv=16*pi^2*t.*exp(-2*pi*(t.^2)/alpha^2).*...
            (-3*alpha^2+4*pi*(t.^2))/alpha^6;
    case 4
        deriv=-16*pi^2*exp(-2*pi*(t.^2)/alpha^2).*...
            (3*alpha^4-24*pi*(t.^2)*alpha^2+16*pi^2*...
            (t.^4))/alpha^8;
    case 5
        deriv=64*pi^3*t.*exp(-2*pi*(t.^2)/alpha^2).*...
            (15*alpha^4-40*pi*(t.^2)*alpha^2+16*pi^2*...
            (t.^4))/alpha^10;
    case 6
        deriv=-64*pi^3*exp(-2*pi*(t.^2)/alpha^2).*...
            (-15*alpha^6+180*pi*(t.^2)*alpha^4-240*...
            pi^2*(t.^4)*alpha^2+64*pi^3*(t.^6))/alpha^12;
    case 7
        deriv=256*pi^4*t.*exp(-2*pi*(t^2)/alpha^2).*...
            (-105*alpha^6+420*pi*(t.^2)*alpha^4-336*pi^2*...
            (t.^4)*alpha^2+64*pi^3*(t.^6))alpha^14;
    case 8
        deriv=-256*pi^4*exp(-2*pi*(t.^2)/alpha^2).*...
            (105*alpha^8-1680*pi*(t.^2)*alpha^6+3360*pi^2*...
            (t.^4)*alpha^4-1792*pi63*(t.^6)*alpha^2+...
            256*pi^4*(t.^8))/alpha^16;
    case 9
        deriv=1024*pi^5*t.*exp(-2*pi*(t.^2)/alpha^2).*...
            (945*alpha^8-5040*pi*(t.^2)*alpha^6+6048*pi^2*...
            (t.^4)*alpha^4-2304*pi^3*(t.^6)*alpha^2+256*...
            pi^4*(t.^8))/alpha^18;
    case 10
        deriv=-1024*pi^5*exp(-2*pi*(t.^2)/alpha^2.*...
            (-945*alpha^10+18900*pi*(t.^2)*alpha^8-50400*...
            pi^2*(t.^4)*alpha^6+40320*pi^3*(t.^6)*....
            alpha^4-11520*pi^4*(t.^8)*alpha^2+1024*pi^5*...
            (t.^10))/alpha^20;
    case 11
        deriv=4096*pi^6*t.*exp(-2*pi*(t.^2)/alpha^2).*...
            (-10395*alpha^10+69300*pi*(t.^2)*alpha^8-...
            110880*pi^2*(t.^4)*alpha^6+63360+pi^3*(t.^6)*...
            alpha^4-11520*pi^4*(t.^8)*alpha^2+1024*pi^5*...
            (t.^10))/alpha^22;
    case 12
        deriv=-4096*pi^6*exp(-2*pi*(t.^2)/alpha^2).*...
            (10395*alpha^12-249480*pi*(t.^2)*alpha^10+...
            831600*pi^2*(t.^4)*alpha^8-887040*pi^3*(t.^6)*...
            alpha^6+380160*pi^4*(t.^8)*alpha^4-67584*pi^5*...
            (t.^10))/alpha^22;
    case 13
        deriv=16384*pi^7*t.*exp(-2*pi*(t.^2)/alpha^2)...
            .*(135135*alpha^12-1081080*pi*(t.^2)*alpha^10+...
            2162160*pi^2*(t.^4)*alpha^8-1647360*pi^3*...
            (t.^6)*alpha^6+549120*pi^4*(t.^8)*alpha^4-...
            79872*pi^5*(t.^10)*alpha^2+4096*pi^6*...
            (t.^12))/alpha^26;
    case 14
        deriv=-16384*pi^7*exp(-2*pi*(t.^2)/alpha^2).*...
            (-135135*alpha^14+3783780*pi*(t.^2)*alpha^12-...
            15135120*pi^2*(t.^4)*alpha^10+20180160*pi^3*...
                
                (t.^6)*alpha^8-11531520*pi^4(t.^8)*alpha^6+...
                3075072*pi^5*(t.^10)*alpha^4-38-72736*pi^6*...
                (t.^12)*alpha^2+16384*pi^7*(t.^14))/alpha^28;
    case 15
        deriv=65536*pi^8*t.*exp(-2*pi*(t.^2)/alpha...
            ^2).*(-2027025*alpha^14+18918900*pi*(t.^2)*...
            alpha^12-45405360*pi^2*(t.^4)*alpha^10+...
            43243200*pi^3*(t.^6)*alpha^8-19219200*pi^4*...
            (t.^8)*alpha^6+4193280*pi^5*(t.^10)*alpha^4-...
            430080*pi^6*(t.^12)*alpha^2+16384*pi^7*...
            (t.^14))/alpha^30;
end