Impulse-doublet sampling of random waveforms

For discrete time systems, the sampling rate is an important design issue. On the one hand, a sampling rate below the Nyquist rate results in spectral aliasing, on the other hand, a sampling rate chosen higher than necessary increases the computational burden. We show in this paper that aliased spectra, arising from sampling a random process below the Nyquist rate, may be completely eliminated. We show that a deterministic or random waveform that is sampled at a rate less than the classical Nyquist rate may be successfully reconstructed if two arbitrarily closely spaced samples are retained each sampling instant. A convergence proof is given for the random waveform case. We suggest a diagonally loaded maximum likelihood estimator approach to reduce the reconstruction errors resulting from timing jitter between the pairs of impulse samples as an area of future research.