Incorrect Impulse Train Waveform Fourier Representation

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As the title suggests, I'm trying to plot the impulse train waveform using its Fourier series complex coefficients. I'm using the Fourier series and Fourier coefficients equations shown below:
My issue is that when trying to plot the impulse train waveform using it's Fourier coefficient, , where A is the amplitude and is the time period of the signal, I end up with a signal that exhibits the same time period, but with N as my amplitude instead of A. See the screenshot below.
Here's the code I'm using.
%% Definition %%
N = 90000; % number of harmonics
t = -10:0.01:10;
T_0 = 4; % time period
w0 = 2 * pi * (1/T_0); % angular frequency
A = 2; % amplitude
%% Summation %%
f = 0;
for n = -N:1:N
c_n = A/T_0;
f_n = c_n * exp(1i*n*w0*t);
f = f + f_n;
end
%% Plotting %%
stem(t, f); % plot f(t)
% axis equal
grid on
line([0,0], ylim, 'Color', 'k', 'LineWidth', 1); % Draw line for Y axis.
line(xlim, [0,0], 'Color', 'k', 'LineWidth', 1); % Draw line for X axis.
xlabel('time (s)');
ylabel('f(t)');
title('Impulse Train')
Table 4.3 defines the Fourier coefficients for various signals. See signal number (7)

Answers (1)

Long He
Long He on 23 Aug 2023
Edited: Long He on 23 Aug 2023
I didn't see any problems or contradictions.
For impulse function , . As you increasing the number of terms, you should see the value becomes bigger and bigger since the impulse train will be better approximated.

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