Let us consider $x_1(t)$, $x_2(t)$, $x_3(t)$, all the same within some some duration 0 to $T$ but all different outside this interval. Now let us multiply each of these signals with $w(t)$, a window function - nonzero from 0 to $T$ but 0 outside this interval. So the multiplication of this $w(t)$ with each of $x_i(t)$ will give the same signal. This should be same as Inverse Fourier Transform of $W(\omega)$ convolved with $X_i(\omega)$. Does this mean convolution of the same signal with different signals can give the same result? Any comments? Is there a pitfall in my interpretation?
Also I see mathematically equations neatly entered in questions and answers on this site? Where should I start to learn on how to write the equations?