A Nearly One-to-One Method to Convert Analog Signals into a Small Volume of Data: First Part: 1-D Signals

The actual quantizing and sampling procedure leads to irreducible errors that do not permit to reconstruct correctly the initial analog signal. To diminish the reconstruction errors to an acceptable level one has to increase the volume of transmitted data. Then, it results in big (or even very big) data volumes that are difficult to store and/or transmit. A deal has been made sometimes between the quality and the resulted data volume in order to have small enough volumes. The paper presents a new (theoretically) one-to-one method to convert physical realizable analog signals into a small volume of data. This method uses the (Shannon) Sampling Theorem, the Bandwidth Compression Theorem and a new Quantizing and Sampling Theorem described in this paper. The Quantizing and Sampling Theorem is based on the properties of phase/frequency modulation and on the properties of a Phase Lock Loop (PLL) to decode also amplitude-modulated signals. Practically, this new method may realize a (theoretically) nearly one-to-one conversion of a physically realizable analog signal into a small volume of data. Adequate software and hardware have to be realized to achieve technically this goal. To diminish the errors of calculus, error- free calculus methods have to be used.