UWB脉冲采用高斯函数的前15阶导数进行组合

% % 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*pi^3*(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^4-14080*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^2+4096*pi^6*(t.^12))/alpha^24; 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^4-372736*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