This paper considers the extension of known sufficient conditions for signal reconstruction from non-uniform periodic samples to the case where the signal comprises a finite combination of sinusoids. In this case, it is shown that the reconstruction can be achieved by a causal observer. The result hinges on the observability of the associated signal model. It is shown that the sufficient conditions for this observability to hold are the same as the band-limited condition which applies to the general non-causal reconstruction result.