# Comparing a signal reconstruction with given equation

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James Stringer on 15 Feb 2016
Answered: Arnab Sen on 23 Feb 2016
I am supposed to compare a signal reconstruction with the given equation g_t = sum(n = 1:20) of g_a*(n/2B)sinc(2piBt-npi) . I am given the values for g_t but mine don't match, can anyone see why? first couple should be 0, 0.016, 0.037...etc
clear; clc
t = 0:0.005:1;
g_t = 0;
g_a = sin(2*pi*t)+(0.5*cos(6*pi*t))+(0.25*cos(18*pi*t));
e_t = 0;
B = 10;
prod1 = 0;
prod7 = 0;
%------------------------------Equation----------------------------------
for n = 1:20
g_t = g_t+(n/20).*g_a.*((sin((2*pi*B*t)-(n*pi)))./((2*pi*B*t)-(n*pi)));
end
e_t = g_a - g_t;
%----------------------------------Plots----------------------------------
figure(1);
hold on;
box on;
plot(t,g_t,'r');
plot(t,g_a,'b');
plot(t,e_t,'y');
ylabel('amplitude g(t)');
xlabel('time t');
title('sync waveform reconstruction');
axis([0 1 -2 2]);
fileID = fopen('Signal Reconstruction.txt', 'w');
fprintf(fileID, '%34s\n','Signal Reconstruction');
fprintf(fileID, '%38s\n','Using Sinc Waveform');
fprintf(fileID, '%2s %8s %7s %9s %7s\n','i','prod1','prod7',...
'gr(t)','delta');
for i = 1:99
fprintf(fileID,'%2.0f %+8.3f %+8.3f %+8.3f %+8.3f\n',i,...
prod1,prod7,g_t(i),e_t(i));
end

Arnab Sen on 23 Feb 2016
Hi James ,
I observe some inconsistency in the definition of 'g_t' and compute of 'g_t' in the code.
I think as per the definition 'g_t' should be as follows:
for n = 1:20
g_t = g_t+(n/2*B).*g_a.*(sinc((2*pi*B*t)));
end