Optimal trade-off between sampling rate and quantization precision in A/D conversion

The jointly optimized sampling rate and quantization precision in A/D conversion is studied. In particular, we consider a basic pulse code modulation A/D scheme in which a stationary process is sampled and quantized by a scalar quantizer. We derive an expression for the minimal mean squared error under linear estimation of the analog input from the digital output, which is also valid under sub-Nyquist sampling. This expression allows for the computation of the sampling rate that minimizes the error under a fixed bitrate at the output, which is the result of an interplay between the number of bits allocated to each sample and the distortion resulting from sampling. We illustrate the results for several examples, which demonstrate the optimality of sub-Nyquist sampling in certain cases.