www.pudn.com > CP0702_GAUSSIAN_DERIVATIVES_E.rar > CP0702_GAUSSIAN_DERIVATIVES_E.M

% 
% FUNCTION 7.4 : "cp0702_Gaussian_derivatives_ESD" 
% 
% Analysis of Energy Spectral Densities of the first 15 
% derivatives of the Gaussian pulse 
% 
% 'smp' samples of the Gaussian pulse are considered, in 
% the time interval 'Tmax - Tmin'  
% 
% The function receives in input the value of the shape 
% factor 'alpha' 
% 
% The function computes and plots the Energy Spectral 
% Densities of the first 15 derivatives of the Gaussian 
% pulse for the 'alpha' value received in input 
%  
% Programmed by Luca De Nardis 
 
function cp0702_Gaussian_derivatives_ESD(alpha) 
 
% ----------------------------------------------- 
% Step Zero - Input parameters and Initialization 
% ----------------------------------------------- 
 
smp = 1024;           % number of samples 
Tmin = -4e-9;         % Lower time limit 
Tmax = 4e-9;          % Upper time limit 
 
N = smp;              % number of samples (i.e. size of 
                      %  the FFT) 
dt = (Tmax-Tmin) / N; % sampling period 
fs = 1/dt;            % sampling frequency 
df = 1 / (N * dt);    % fundamental frequency 
 
t=linspace(Tmin,Tmax,smp); % Inizialization of the time 
                           % axis 
 
F=figure(1); 
set(F,'Position',[100 190 650 450]); 
 
for i=1:15 
 
% ------------------------------------------------------ 
% Step One - Amplitude-normalized pulse waveforms in the 
%            time domain 
% ------------------------------------------------------ 
 
    % Determination of the i-th derivative 
    derivative(i,:)=cp0702_analytical_waveforms(t,i,alpha); 
    % Amplitude normalization of the i-th derivative 
    derivative(i,:)=derivative(i,:) / ... 
       max(abs(derivative(i,:))); 
 
% ---------------------------------------------------- 
% Step Two - Analysis in the frequency domain and data 
%            plotting 
% ---------------------------------------------------- 
 
    % double-sided MATLAB amplitude spectrum 
    X=fft(derivative(i,:),N); 
    % conversion from MATLAB spectrum to Fourier spectrum 
    X=X/N; 
    % DOUBLE-SIDED ESD 
    E = fftshift(abs(X).^2/(df^2)); 
    % SINGLE-SIDED ESD 
    Ess = 2 * E((N/2+1):N); 
    frequency=linspace((-fs/2),(fs/2),N);  
     
    % Positive frequency axis 
    positivefrequency=linspace(0,(fs/2),N/2); 
    PF=semilogy(positivefrequency,Ess); 
    set(PF,'LineWidth',[2]); 
    hold on 
end 
 
% ---------------------------------------- 
% Step Three - Graphical output formatting 
% ---------------------------------------- 
 
axis([0 1.25e10 1e-55 1e-15]); 
AX=gca; 
set(AX,'FontSize',12); 
GT=title('Frequency domain'); 
set(GT,'FontSize',14); 
X=xlabel('Frequency [Hz]'); 
set(X,'FontSize',14); 
Y=ylabel('ESD  [(V^2)*sec/Hz]'); 
set(Y,'FontSize',14); 
alphavalue = {'\alpha = 0.714 ns'}; 
derivebehaviour = {'Increasing differentiation order'};  
text(7e9, 1e-28, derivebehaviour,'BackgroundColor',... 
   [1 1 1]); 
text(0.5e9, 3e-17, '1^{st} derivative',... 
   'BackgroundColor', [1 1 1]); 
text(4e9, 3e-17, '15^{th} derivative',... 
   'BackgroundColor', [1 1 1]); 
text(2e9,10e-48,alphavalue,'BackgroundColor', [1 1 1]);