Restoration of double-impulse sampled signals at one-half the Nyquist rate

A generalised version of the Nyquist sampling theorem admits sampling at an average rate equal to twice the highest frequency component of the sampled signal. For example, we may envision a sampling structure wherein a pair of closely spaced impulses perform the signal sampling, each impulse pair sampling the signal at one-half the minimum rate required for ideal impulse sampling. We next derive a frequency domain restoration algorithm and its corresponding time domain interpolation formula. Finally, we quantify the effect of impulse pair spacing on the numerical conditioning of the restoration algorithm. Simulations results are provided for reconstruction of several tests signals and a bandlimited random process.