Fourier Analysis: Derivation of Fourier Transform

1. From Fourier Series to Fourier Transform
    A continuous-time periodic square wave:

    A aperiodic signal can be considered as a special periodic signal whose period is infinite.
    The envelop of the Fourier Series coefficients remains the same if we fix the zerocrossing
    In the limit case when the period approaches infinite, the FS coefficients should become a continuous function as the envelop.













Fourier Series-->
    
Envelop-->

Then-->

2. Any finite duration signal can be considered as a periodic signal whose period is infinite