A question on Fourier Series and the frequency of the sinusoids On studying about Fourier series, I encountered 2 doubts:


How is it that a non-periodic function has a Fourier series?
When expressing a periodic function as summation of sinusoids, why is the fundamental (minimum) frequency taken to be that of the periodic signal? Why cannot one of the sinusoids have a frequency less than the fundamental?


I mean, we think of representing the signal in terms of sinusoids with frequencies greater than and equal to the fundamental frequency, and of course, there is the DC part as well. But, why is there no sinusoid with frequency less than the fundamental as well?

Is there any mathematical logic for the second point?
A function that is not periodic doesn't have a Fourier series. What you can do is take a finite length interval and construct a Fourier series which approximates the function in that interval (and continues it periodically outside that interval).
The sum of several sinusoids with one of the sinusoids having (fundamental) period $T$ can never have a period less than $T$, simply because that one sinusoid will destroy periodicity (with period $&lt;T$) due to its larger period.