Incorrect Impulse Train Waveform Fourier Representation

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)

Answer 1

[VBBV]

%if true
%%Definition %%
N = 90000;  % number of harmonics
t = -10:2:10;
T_0 = 4;  % time period
w0 = 2 * pi * (1/T_0); % angular frequency
A = 2;  % amplitude 
%%Summation %%
  c_n = A/T_0;
  f_n= c_n * exp(1i*N*w0.*t);

Plotting %%

stem(t, f_n); % 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')

You don't need a for loop on this case. The result produces pulse train with amplitude of 0.5 since amplitude is given by A/T_0 i.e 2/4

[Obadah M.]

The 0.5 impulses appear on every t value. Shouldn't it appear every ?

[VBBV]

If you want amplitude as A then you need to use

%if true
c_n = A;
f_n = c_n*exp(1i*N*w0.*t)

[Obadah M.]

The impulses should appear every ... Which is not the case here... What I'm getting instead is an impulse at each and every t value. I don't think that's how it should be.

[Obadah M.]

Any further suggestions are much appreciated.