I know that all periodic continuous time signal have discrete spectral representations, but are all discrete spectral representations periodic in continuous time?
Also, can all periodic signals be represented by a fourier series?
2026-04-03 09:25:17.1775208317
Continuous time signal and Discrete time signal
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Nope! Consider:
$$\cos(t)+\cos(\pi t) $$
It's Fourier transform is certainly discrete, but the signal isn't periodic because $\pi$ is irrational. No integer multiple of periods is going to get you back to where you started.