EE5410 Signal Processing -- How to represent aperiodic signals?
1. Whereas for periodic signals the complex exponential building blocks are harmonically related, for aperiodic signals they are infinitesimally close in frequency, and the representation in terms of a linear combination takes the form of an integral rather than a sum.
2. Fourier reasoned that an aperiodic signal can be viewed as a periodic signal with an INFINITE period.
3. As the period increases, the fundamental frequency decreases and the harmonically related components becomes closer in frequency.
4. As the period becomes INFINITE, the frequency components for a continuum and the Fourier series sum becomes an integral.