The problem is stated below. enter image description here

However, our lecturer did not cover much on the Fourier transform coefficients, and I don't know where to start. Could anyone show me a way to approach this problem? Thanks.


Every function with period $2/3$ also has $2$ as a (non-primitive) period, combining $3$ of the shorter periods. The same goes for functions with period $1/2$, $4$ periods of that give a period of $2$. And $2$ is the smallest common period for the periods one starts with (cue the holy hand-grenade of Antioch).

For everything else please report back to the instructor, obviously the formulation of the task is garbage since there are no signals in the description. Or some context is missing.

One sensible task could be to relate the Fourier series formulas for signals with the indicated periods, which mostly amounts to the introduction of coefficients zero to fill the gaps. However, what role the lcm plays is not quite as obvious.

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