Window functions and the Fourier transform I want to clarify the 'correct' way to use windowing and Fourier transforms. 

My question is somewhat related to this one, but I have a few additional queries.

I have some real, non periodic signal in the time domain $y(t)$. Since this is a real signal, the data is naturally discrete.

I want to calculate the Fourier transform of this signal, $Y(f)$, within an observation time, $T$. I understand that

$$ \tilde{Y}(f) = \int^{+T/2}_{-T/2} y(t) \exp(-2 \pi i f t) dt $$

$$ = Y(f) \ast T \operatorname{sinc} (\pi f T)$$

where $Y(f)$ is the unwindowed FT of the infinite signal

To avoid the effects of the $\operatorname{sinc}$ function, windowing is recommended to taper the signal within the observation period $T$.

My question is: If I want to calculate $\tilde{Y}(f)$ computationally (e.g. using python/numpy), 


Is it required for the time signal to be zero at the edges? Why so? 
Does spectral leakage still occur if so? 
Aren't we distorting the true time signal $y(t)$?
If we increase the observation time $T$ to e.g. $2T$, how does $\tilde{Y}(f)$ change?
So called spectral leakage always occurs when transforming any finite length observation.  That's because it's an artifact of windowing, and any non-infinite length observation (-t/2 ... +t/2) requires some sort of window, inherent rectangular or otherwise.  A window function allow you to choose your artifact: from window "distortion" to Sinc effects, and/or many other choices.