1. As T increases, or equivalently, as the fundamental frequency w0 =2*PI/T decreases, the envelope is sampled with a closer and closer spacing.
2. As T becomes arbitrarily LARGE, the original periodic square wave approaches a rectangular pulse ( ie., all that remains in the time domain is an aperiodic is an aperiodic signal corresponding to ONE period of the square wave. )
3. Also, the Fourier series coefficients, multiplied by T, become more and more closely spaced samples of the envelop, so that in some sense the set of Fourier series coefficients approaches the envelope function as T --> INFINITY.
4. We think of an aperiodic signal as the LIMIT of a periodic signal as the period becomes arbitrarily large, and we examine the limiting behaviour of the Fourier series representation for the signal.