step_files

====================================================================================
Copy the following MATLAB code into .m file
====================================================================================

clc
close all
clear all

ns = 1e-9;
fsize = 20;

% Load the analytical and simulated step responses
D_analyt = csvread('z_step_analytical.csv');
t_a    = D_analyt(:,1);
step_a = D_analyt(:,2);

D_simul  = csvread('z_step_simulated.csv');
t_s    = D_simul(:,1);
step_s = D_simul(:,2);

% define the sampling interval
si_a = mean(diff(t_a));
si_s = mean(diff(t_s));
si = si_s;


% Plot analytical and simulated Step responses
figure(1)
clf
hold on;
grid on;
set(gca, 'FontSize', fsize);
plot(t_a/ns, step_a, 'g', 'disp', 'analytical', 'linewidth', 2)
plot(t_s/ns, step_s, 'r', 'disp', 'Simulated', 'linewidth', 2)
legend('show', 'Location', 'SouthEast')
xlabel('time, ns');
ylabel('Amplitude, V')
title('Step Response')

%% Reconstruct step from the analytical step (This works)

% calculate impulse from step by using diff
ir_a = diff([step_a; step_a(end)])/si ;

% get the discrete system polynomials (B and A) from IR
[BB_a, AA_a] = prony(ir_a *si, 2, 2);

% reconstruct the system SR from polynomials (B and A)
sys_a = tf(BB_a, AA_a, si, 'variable','z^-1');

[step_a_recons]= step(sys_a, t_a);

figure(2)
clf
hold on;
grid on;
set(gca, 'FontSize', fsize);
plot(t_a/ns, step_a       , 'g'  , 'disp', 'initial'      , 'linewidth', 2)
plot(t_a/ns, step_a_recons, 'k-.', 'disp', 'reconstructed', 'linewidth', 2)
legend('show', 'Location', 'SouthEast')
xlabel('time, ns');
ylabel('Amplitude, V')
title('Analytical Step Response')

%% Reconstruct step from the simulated step (This does not work)

% Trim the beginning of simulated step response
idx_start = 529;
step_s_cut = step_s(idx_start:end);
t_s_cut = t_s(idx_start:end);
t_s_cut = t_s_cut - t_s_cut(1);

% calculate impulse from step by using diff
ir_s = diff([step_s_cut; step_s_cut(end)])/si ;

% get the discrete system polynomials (B and A) from IR
[BB_s, AA_s] = prony(ir_s *si, 2, 2);

% reconstruct the system SR from polynomials (B and A)
sys_s = tf(BB_s, AA_s, si, 'variable','z^-1');

[step_s_recons]= step(sys_s, t_s_cut);


figure(3)
clf
hold on;
grid on;
set(gca, 'FontSize', fsize);
plot(step_s, 'r-', 'disp', 'initial', 'linewidth', 2)
plot(idx_start + (0:length(step_s_cut)-1), step_s_cut, 'b--', 'disp', ['trimmed, i=', num2str(idx_start)], 'linewidth', 2)
legend('show', 'Location', 'SouthEast')
xlabel('samples');
ylabel('Amplitude, V')
title('Simulated Step Response')
set(gcf,'Position',[400 150 636 476]);

figure(4)
clf
hold on;
grid on;
set(gca, 'FontSize', fsize);
plot(t_s_cut/ns, step_s_cut,    'b', 'disp', 'initial (trimmed)', 'linewidth', 2)
plot(t_s_cut/ns, step_s_recons, 'm-.', 'disp', 'reconstructed', 'linewidth', 2)
legend('show', 'Location', 'SouthEast')
xlabel('time, ns');
ylabel('Amplitude, V')
title('Simulated Step Response')




====================================================================================
Copy the following data into z_step_analytical.csv
====================================================================================

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 9.765625000e-13, 1.666973223e-02
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====================================================================================
Copy the following data into z_step_simulated.csv
====================================================================================
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