When Does Periodicity in Discrete-Time Imply that in Continuous-Time?

If the sampled version <tex>$x(n)=x_{c}(nT)$</tex> of a continuous-time signal <tex>$x_{c}(t)$</tex> is periodic, it does not necessarily imply that <tex>$x_{c}(t)$</tex> is periodic. This paper presents some conditions under which periodicity of <tex>$x_{c}(t)$</tex> is indeed implied. The conditions for this implication are more relaxed than bandlimitedness. The results place in evidence a multriate method to estimate the period of <tex>$x_{c}(t)$</tex> from the samples <tex>$x(n)$</tex>. The method works better than DFT based methods when the available data segment is short and multiple hidden periods are to be estimated.

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