How to programmatically generate a simple rectangular radio pulse?

Question

C++ / C#

They gave the task: to generate a signal: a simple rectangular radio pulse. It needs to be done in C++
. I found an expression that describes this signal:

where

I can't figure out what i is in the formula. E - amplitude. I still can’t understand what should be equal to t at the beginning and what is the gain. If anyone knows, please explain.

Answer 1

The formula uses Euler's formula to write orthogonal sine and cosine in complex form.
You only need the real part.
In fact, you are just drawing a sinusoid of duration T.

Answer 2

i is the imaginary unit. t, obviously, it makes sense to consider the interval from -T ₀ /2 to T ₀ /2.

Answer 3

this is how I transferred the formula to c++

if(qAbs(time)>T/2)
    {
        u = 0;
    }
    else
    {
        u = 1*qExp(2*3.1415/T*time);
    }
    time+=0.1;
    if(time>T/2) time = -T/2; //тут скорее всего неверно сделано

Runs in a separate thread.
As a result, it draws like this:
but it is necessary like this: