Quantizing theorem

Actually, signals are sampled and quantized for their digital transmission and/or processing. A sampling theorem (due to Shannon) allows to theoretically reconstruct the sampled signal without errors. As an equivalent quantizing theorem does not yet exist, one increase the number of transmitted quanta to diminish the transmitted error to an acceptable value. It can be observed that a quantizing process is equivalent to a generalized phase/frequency modulation. This leads to a quantizing theorem and allows to code/decode, theoretically without errors, an analog signal of limited frequency bandwidth into a quantized signal of also limited frequency bandwidth and vice-versa. It can be remarked that practically, only limited frequency bandwidth signals may be used in practical transmissions. To exemplify this theorem we presents some simple examples in simulation. As extension, a method to convert the amplitude-modulated part of a signal into its phase/frequency-modulated part and vice-versa is also presented. A method to diminish the errors of actual sampling and quantizing coder/decoder is also presented. These may be useful to improve actual quantizing coder/decoder and keeping then the same (and/or better) quality of transmission for a smaller number of quanta. It wills leads also to diminish the volume of a quantized signal and also to a better utilization of the transmitting channels spectrum.