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Observational data often is irregularly taken or has large gaps due to instrument failure or other real world effects. Yet no spectral estimation theory in use allows one, without dubious interpolation, to estimate spectra from an irregularly sampled signal, nor to combine pieces of record to estimate power at periods longer than the longest piece. A natural extension of conventional complex demodulation is proposed and illustrated for estimating auto- and cross-spectra. The sampling times can be randomly spaced and need not even be in order. The method reduces to the usual method when the data are equally spaced.