Spectrum Analyzer measurement principles' question

Hi, Folks:

I am curious about how machine spectrum analyzer calculate the PSD of input signal.

In Parcevall law:

∫Φ(t)2dt = ∫Φ(s)2ds ;

In left side of equation, original law said that the integration start from -T to +T. (T is measurement interval)

However, in real world, Φ(t) is always zero when time is negative.

So, the final PSD is get from divide both sides by T, or 2T?

I think it should be T, is that right?