A signal containing no pure sinusoidal components

I'm trying to decipher what exactly this statement means. So if I have a signal which has no pure sinusoidal components, does that mean I can't decompose my signal completely into sine-waves which may be amplitude/phase/period shifted? And so I would conclude that there is also like a saw-tooth component or a square-function component mixed up in the signal as well?

Saying that the signal contains NO pure sinusoidal component makes me feel like its decomposition should not include ANY amplitude/phase/period shifted sine-waves.. but that seems a little extreme.

Could someone clarify this for me? Thanks.

• Some pathological function that was not integrable might not have a Fourier transform. Otherwise wouldn't the existance of an FT of any non-DC signal imply that it did contain at least 1 pure sinusoid? – hotpaw2 May 4 '12 at 5:46