Noise-shaped quantization for nonuniform sampling

The Nyquist theorem (for perfect reconstruction of a band-limited signal from its noiseless samples) depends, essentially, only on the average sampling rate. In contrast, reconstruction from imperfect samples strongly depends also on the sampling pattern. Specifically, when the samples are corrupted with independent noise, the reconstruction distortion is generally higher for nonuniform sampling than for uniform sampling at the same average rate - a phenomenon known as 'noise amplification'. We show that this degradation in performance can be avoided if the noise spectrum can be controlled; for any periodic nonuniform sampling pattern, there exists a quantization noise-shaping scheme that mitigates the noise amplification. Moreover, a scheme that combines noise shaping, Wiener filtering and entropy-coded dithered quantization (ECDQ) achieves the rate-distortion function of a (white or colored) Gaussian source, up to the granular loss of the lattice quantizer. This loss tends to zero, for a sequence of good latices, as the lattice dimension tends to infinity.