Decomposition of apriodic and periodic signals

[Geek007]

Hi there,
why the decomposition of periodic Composite signal give discrete frequencies and decomposition of aperiodic signal give continuous(in decimal) frequencies. please kindly do explain the concept behind in as simple words possible.
Thanks

 

[blue_leaf77]

One hand wavy argument makes use the period of the signal as the key tool. Let's say there is a periodic signal with period $T$, then in the frequency domain, adjacent frequency components are separated by $M\pi/T$ where $M$ is an integer. As for a nonperiodic signal, we can view it as a periodic signal with infinitely long period, $T \to \infty$. Therefore, the separation between adjacent frequency components will be $\lim_{T\to \infty} M\pi/T = 0$, yielding a continuous spectrum.