The optimality of variable sampling schemes for a digital encoder
Paul P. Wang · International Journal of Control · 1973
Regardless of simplicity in both structure and hardware, conventional digital modulators such as delta modulation and its modified forms, etc., have not yet been proven efficient. This is primarily due to the large magnitude of the resultant quantized noise. This paper, by invoking the maximum principle of Pontryagin, presents a novel digital encoder with variable sampling. The design criteria chosen is minimization of integrated quantized noise power since the major challenge for an efficient digital modulator is reduction of quantized noise. As it turns out, the resultant optimal systems can be identified from the discrete control systems point of view as belonging to the second type of PFM (pulse frequency modulation). Several possible implementations of the systems are suggested and the expected quality of performance is also discussed and predicted. Finally, the comparison of the optimal system with the conventional existing system is included for immediate reference.